The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.
To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:
Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.
(-14) + x + 14 = 14 + 14
x = 28
The solution to the equation (-14) + x = 14 is x = 28.
In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.
Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:
(-14) + 28 = 14
14 = 14
The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The linear inequality represented by the graph is y < 3x + 2. Option A.
To determine the linear inequality represented by the graph, let's analyze the given information and the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.
We are given two points on the line: (-3, -7) and (0, 2). Using these points, we can calculate the slope (m) as follows:
m = (y2 - y1) / (x2 - x1)
= (2 - (-7)) / (0 - (-3))
= 9 / 3
= 3
Therefore, the slope of the line is 3.
Next, we can substitute the slope and one of the given points into the slope-intercept form to find the y-intercept (b). Let's use the point (0, 2):
y = mx + b
2 = 3(0) + b
2 = b
So, the y-intercept (b) is 2.
Now we have the equation of the line: y = 3x + 2.
The shaded region is to the left of the line. To express this region as an inequality, we need to find the inequality symbol. Since everything to the left of the line is shaded, we need the inequality to represent values less than the line.
Therefore, the correct inequality is y < 3x + 2.
Hence, the linear inequality represented by the graph is y < 3x + 2. So Option A is correct.
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Note the complete question is
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
A.) y < 3x + 2
B.) y > 3x + 2
C.) y < 1/3x + 2
D.) y > 1/3x + 2
When five times a number is decreased by 8, the result is 37. What is the number?
Answer:
5n - 8 = 37
5n = 45
n = 9
The number is 9.
what is the value of m
The value of m<RQS as required to be determined in the task content is; 70°.
What is the value of m<RQS as required to be determined?It follows from the task content that the measure of angle RQS is to be determined as required.
Recall, the measure of the central angle subtended by an arc is twice that which it subtends at any point on the circumference.
Therefore, m<RPS = 2 • m<RQS.
m<RQS = 140°/2
m<RQS = 70°.
Ultimately, the measure of angle RQS are; 70°.
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9
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = -x + 7
y
9
8
X
0
3
6
9
y
5
6
7
8
X
-6
-3
0
3
7
6
The equation that represents the other equation is y= 1/3
The solution of the system is (
)
X+
Reset
5
Next I
Pls help I need this answer
The equivalent expressions for this problem are given as follows:
(4x³ + 7x - 4) - (2x³ - x - 8): B.[tex](x^4 - 3x^2 + x) + (2x^4 + 4x - 7)[/tex]: D.2x³ - x² - 6x: A.How to obtain the equivalent expressions?Equivalent expressions are the expressions that have the same result, hence we must simplify each expression.
The first expression is given as follows:
(4x³ + 7x - 4) - (2x³ - x - 8).
Simplifying the like terms, we have that:
4x³ - 2x³ = 2x³.7x - (-x) = 7x + x = 8x.-4 - (-8) = -4 + 8 = 4.Hence it is equivalent to expression B.
The second expression is simplified as follows:
[tex](x^4 - 3x^2 + x) + (2x^4 + 4x - 7) = 3x^4 - 3x^2 + 5x - 7[/tex]
The third expression is simplified as follows:
(x² - 2x)(2x + 3) = 2x³ + 3x² - 4x² - 6x = 2x³ - x² - 6x.
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According to these three facts, which statements are true?
HELP PLEASE !!!
The correct statements are: B. Circle F and circle D are similar and D. The center of circle F is (0, 3).
Explanation:
A. The radius of circle F is not 28. When a circle is translated, the radius remains the same. So, circle F has the same radius as circle D, which is 7.
B. Circle F and circle D are similar. Similarity means that the two shapes have the same shape but possibly different sizes. Since circle F is a translation of circle D, it has the same shape and proportions as circle D. Therefore, they are similar.
C. Circle F and circle D are not congruent. Congruence means that two shapes are identical in both shape and size. While circle F and circle D have the same shape, they have different positions due to the translation. Thus, they are not congruent.
D. The center of circle F is (0, 3). When a circle is translated horizontally by a certain amount, the x-coordinate of the center changes, while the y-coordinate remains the same. Since circle F is translated 2 units to the right, the x-coordinate of the center of circle F would be 2 + 0 = 2. As the y-coordinate remains the same, the center of circle F is (2, 3). Therefore, the statement is incorrect.
In summary, the correct statements are B and D. Circle F and circle D are similar, and the center of circle F is (0, 3). Therefore, Option B and D are correct.
The question was incomplete. find the full content below:
According to these three facts, which statements are true?
• Circle D has center (2, 3) and radius 7.
• Circle F is a translation of circle D, 2 units right.
• Circle F is a dilation of circle D with a scale factor of 4.
Select each correct answer.
A. The radius of circle F is 28.
B. Circle F and circle D are similar.
C. Circle F and circle D are congruent.
D. The center of circle F is (0, 3)
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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 29, 31, 49, 37, 26, 28. Use a 0.025 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.
Step 1: Set up hypotheses
H₀: The outcomes of the die are equally likely.
H₁: The outcomes of the die are not equally likely.
Step 2: Select the significance level
The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.
Step 3: Compute the test statistic
We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.
Expected frequencies (fair die):
1: 200/6 = 33.33
2: 200/6 = 33.33
3: 200/6 = 33.33
4: 200/6 = 33.33
5: 200/6 = 33.33
6: 200/6 = 33.33
Applying the chi-square formula, we get the test statistic:
χ² = ∑((observed - expected)² / expected)
Calculating this value, we get χ² ≈ 13.97.
Step 4: Determine the critical value
Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.
Step 5: Make a decision
The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.
The loaded die appears to behave differently from a fair die.
In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
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What’s equivalent to 6 to the -3 power
Statement: Reasons:
DF=EG.
DE
Prove: DE=FG
Statements
DF=EG
DF=DE+EF.
EG=EF+FG
DE+EF=EF+ FG
FL
G
Answer:
az
Step-by-step explanation:
if you apply the changes below to the quadratic pareent function, F(x)=x^2 what is the equation of the new function? shift 6 units right. shift 4 units down.
The equation of the new function after shifting 6 units right and 4 units down is f(x) = (x + 6)² - 4.
If we are to apply the changes below to the quadratic parent function, F(x) = x², what is the equation of the new function, given that we are to shift 6 units to the right and 4 units down? We will approach this question by following the steps outlined below.
Step 1: Identify the parent function F(x) = x² and its transformations
Step 2: Write the equation of the new function
Step 3: Simplify the new equation of the function.Step 1: Identify the parent function F(x) = x² and its transformations
Here, we are given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down.
The general equation for the horizontal and vertical shifts of a quadratic function is given by:f(x) = a(x - h)² + k, where a, h, and k are constants.
The value of a determines the direction of opening of the parabola, while (h, k) represents the vertex of the parabola.
If a > 0, the parabola opens upwards, while a < 0, the parabola opens downwards. If the values of (h, k) are positive, the parabola is shifted right and up, respectively. On the other hand, if the values of (h, k) are negative, the parabola is shifted left and down, respectively.
Therefore, given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down, we can represent these changes by the following:
a = 1 (since the parabola opens upwards)h = -6 (since we are shifting the parabola 6 units to the right)k = -4 (since we are shifting the parabola 4 units down)
Step 2: Write the equation of the new function Now that we have identified the constants a, h, and k, we can write the equation of the new function as follows:f(x) = a(x - h)² + kf(x) = 1(x - (-6))² + (-4)Replacing the constants a, h, and k in the equation, we have:f(x) = (x + 6)² - 4
Step 3: Simplify the new equation of the function.f(x) = (x + 6)² - 4= (x + 6)(x + 6) - 4= x² + 12x + 36 - 4= x² + 12x + 32Therefore, the equation of the new function after shifting 6 units right and 4 units down is f(x) = x² + 12x + 32.
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NO LINKS!! URGENT HELP PLEASE!!
25. Use the relationship in the diagrams below to solve for the given variable.
Justify your solution with a definition or theorem.
Answer:
x = 110°
Step-by-step explanation:
The opposite angles are equal in a parallelogram
3x - 60 = 2x + 50
⇒ 3x - 2x = 60 + 50
⇒ x = 110°
Answer:
x = 110°
Step-by-step explanation:
As the top and bottom line segments of the given shape are the same length and parallel (indicated by the tick marks and arrows), the shape is a parallelogram.
As the opposite angles of a parallelogram are equal, to find the value of the variable x, equate the two angle expressions and solve for x:
[tex]\begin{aligned}3x-60^{\circ}&=2x+50^{\circ}\\3x-60^{\circ}-2x&=2x+50^{\circ}-2x\\x-60^{\circ}&=50^{\circ}\\x-60^{\circ}+60^{\circ}&=50^{\circ}+60^{\circ}\\x&=110^{\circ}\end{aligned}[/tex]
Therefore, the value of x is 110°.
Note: There must be an error in the question. If x = 110°, each angle measures 270°, which is impossible since the sum of the interior angles of a quadrilateral is 360°.
Triangles J K L and M N R are shown. In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS? ∠J ≅ ∠M ∠L ≅ ∠R ∠K ≅ ∠N ∠R ≅ ∠K
To show that ΔJKL ≅ ΔMNR by SAS (Side-Angle-Side), we need the additional information that the lengths of the corresponding sides JK and MN are equal.
To prove ΔJKL ≅ ΔMNR using the SAS congruence criterion, we need to establish that two corresponding sides and the included angle of the triangles are congruent.
1. Given information:
- KL ≅ NR (corresponding sides)
- JL ≅ MR (corresponding sides)
- ∠J ≅ ∠M (included angle)
- ∠L ≅ ∠R (corresponding angles)
- ∠K ≅ ∠N (corresponding angles)
- ∠R ≅ ∠K (corresponding angles)
2. Additional information needed:
- We need to know if JK ≅ MN (corresponding sides) to establish the SAS congruence criterion.
3. Possible scenarios:
- If JK ≅ MN, then we can establish that ΔJKL ≅ ΔMNR by SAS.
- If JK is not equal to MN, then we cannot apply the SAS congruence criterion, and additional information or a different congruence criterion would be needed to prove the triangles congruent.
In summary, the lengths of the corresponding sides JK and MN need to be equal to prove ΔJKL ≅ ΔMNR by SAS. Without this information, we cannot conclude the congruence of the triangles using the SAS criterion alone.
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Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
Given the information in the diagram, the theorem that best justifies why lines j and k must be parallel include the following: D. converse alternate exterior angles theorem.
What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
In Mathematics and Geometry, the alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
Since the alternate exterior angles are congruent, we can logically deduce the following based on the converse alternate exterior angles theorem;
93° ≅ 93° (lines j and k are parallel lines).
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Complete Question:
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
alternate interior angles theorem
alternate exterior angles theorem
converse alternate interior angles theorem
converse alternate exterior angles theorem
Determine the equation of the circle graphed below 100pts pls
Answer:
(x + 5)² + (y – 1)² = 25
Step-by-step explanation:
Note that the general equation of a circle is (x – h)² + (y – k)² = r², where (h, k) represents the location of the circle's center, and r represents the length of its radius.
The circle is 10 units in diamater, so the radius is half this: r=10/2=5.
The circle goes from -10 to 0 along the x-axis, so the x-coordinate of its centre is halfway between this: h=(-10+0)/2=-10/2=-5
The circle goes from -4 to 6 along the y-axis, so the y-coordinate of its centre is halfway between this: k=(-4+6)/2=-2/2=1
Now that we know r, h, and k, we can sub these into the general formula to get our equation:
(x - (-5))² + (y – 1)² = 5²
(x + 5)² + (y – 1)² = 25
Two square-shaped fields are next to each other. The perimeter of each field is 36 feet. The two fields are joined together to form a single rectangular field. What is the perimeter of the rectangular field? (1 point) a 72 feet b 63 feet c 54 feet d 45 feet
Answer:
c) 54 feet
Step-by-step explanation:
Let the side of the square be x
perimeter = 4x
⇒ 36 = 4x
⇒ x = 36/4 = 9 feet
Each side is 9 feet
When we join the two squares, it becomes a rectangle with
b = 9
l = 9 + 9 = 18
The perimeter of a rectangle is 2(l + b)
perimeter = 2(18 + 9)
= 2(27)
= 54 feet
Answer:
Option (c) 54 feet
Step-by-step explanation:
Perimeter of one square is 36 feet.
Side of square = 36 / 4 = 9 feet
When combined together one side of each square merged.
So, the perimeter of rectangular shape will be;
(9+9+9) + (9+9+9)
27 + 27
54 feet.
what is the 20th term of the sequence that begins -4, 8, -16, 32...?
Answer:
-2097152 is the 20th term
Step-by-step explanation:
Write geometric sequence as an explicit formula
[tex]-4,8,-16,32\rightarrow-4(-2)^0,-4(-2)^1,-4(-2)^2,4(-2)^3\\a_n=a_1r^{n-1}\rightarrow a_n=-4(-2)^{n-1}[/tex]
Find the n=20th term
[tex]a_{20}=-4(-2)^{20-1}=-4(-2)^{19}=4(-524288)=-2097152[/tex]
Predict the number of sales in month 5
The predicted sales in month 5 is -2778.
Obtaining the linear equation which models the data :
y = bx + cb = slope = (y2-y1)/(x2-x1)
b = (926-7408)/(4-1)
b = -2160.67
c = intercept ;
taking the points (x = 2 and y = 3704)
Inserting into the general equation:
3704 = -2160.67(2) + c
3704 = -4321.33 + c
c = 3704 + 4321.33
c = 8025.33
General equation becomes : y = -2160.67x + 8025.33
To obtain sales in month 5:
y = -2160.67(5) + 8025.33
y = -2778
Hence, the predicted sales in month 5 is -2778.
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What is the first step in solving ab -c = d for a
Answer:
See below
Step-by-step explanation:
To solve for "a", you would first isolate ab on the right-hand side by adding "c" on both sides:
[tex]ab-c=d\\ab-c+c=d+c\\ab=d+c[/tex]
Next, you would divide both sides by "b" to isolate "a":
[tex]ab=d+c\\ab\div b=(d+c)\div b\\a = \frac{d+c}{b}[/tex]
The solution is:
[tex]\large\boldsymbol{a = \dfrac{d + c}{b}}[/tex]Work/explanation:
To solve the given expression for a, we should isolate it by using basic algebraic operations.
The first step is to add c to each side:
[tex]\sf{ab-c=d}[/tex]
[tex]\sf{ab=d+c}[/tex]
Now, divide each side by b:
[tex]\sf{a=\dfrac{d+c}{b}}[/tex]
I have solved the equation for a.
Thrrefore, the answer is a = d + c / b.What is the solution to the system of equations graphed below?
A. (0, -1)
OB. (0,1)
OC. (-1,0)
D. (1,0)
S
PRE
y=-x-1
y=x+1
y=x+1
y=-x-1
The point of intersection is (-1, 0). Therefore, the correct answer is C. (-1, 0).
To find the solution to the system of equations graphed below, we need to identify the point where the two lines intersect.
The equations of the lines are:
y = -x - 1
y = x + 1
To find the point of intersection, we can set the two equations equal to each other and solve for x:
-x - 1 = x + 1
Adding x to both sides:
-1 = 2x + 1
Subtracting 1 from both sides:
-2 = 2x
Dividing both sides by 2:
x = -1
Now that we have the x-coordinate, we can substitute this value back into either equation to find the y-coordinate. Let's use the second equation:
y = x + 1
y = -1 + 1
y = 0
Therefore, the point of intersection is (-1, 0).
Among the given options, the closest point to (-1, 0) is option C: (-1, 0).
Therefore, the correct answer is C. (-1, 0).
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williams has 32 coins that are all either quarter or dimes the coins have a value of $5 how many dimes does williams have
Answer:
20 dimes
Step-by-step explanation:
1 dime = $0.1
1 quarter = $0.25
Let there be x dimes
Then the number of quarters is 32-x
Also, $5 = 0.1x + 0.25(32-x)
⇒ 5 = 0.1x + 8 - 0.25x
⇒ 0.25x - 0.1x = 8 - 5
⇒ 0.15x = 3
⇒ x = 3/0.15
⇒ x = 20
AB=BC
A
60°
ODC
D
AB
374
B
The longest segment shown is
BC
C
Note that the longest segment in the shapes shown is DC (Option B).
How is this so?The longest side of a triangle is opposite to greatest angle.
To determine the longest side in a triangle, compare the lengths of all three sides. The side with the greatest length is the longest side.
You can use a ruler or a measuring tool to measure the lengths of the sides or compare the numerical values if they are provided.
In this case,
∠A = ∠DBA = 60°
So ∠ ABD is an equilateral triangle.
So, AB = BD = AD
Since
AB = BC
Then
∠BDC = ∠C ∠ 38°
so ∠DBC > 90°
This means that DC is the longest side.
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When is it better to have a session pass versus just paying general admission?
After 8 visits: How much would each person pay? Show your work for calculations.
Session Pass______? General Admission______?
After 10 visits: How much would each person pay? Show your work for calculations.
Session pass _____? General Admission_____?
After 8 visits: General Admission: Each person would pay $200. Annual Public Session Pass: Each person would pay $299.
After 10 visits: General Admission: Each person would pay $250. Annual Public Session Pass: Each person would still pay $299.
To determine when it is better to have a session pass versus just paying general admission, we need to compare the costs for each option.
General Admission with skate rental: $25
Annual Public Session Pass with skate rental: $299
After 8 visits:
For General Admission, the cost per visit would be $25 per visit.
Total cost for 8 visits: $25 x 8 = $200
For the Annual Public Session Pass, the cost is a one-time payment of $299, regardless of the number of visits. Therefore, after 8 visits, the cost remains the same at $299.
Therefore, after 8 visits, it would be more cost-effective to have the Annual Public Session Pass as the cost per person would be $299.
After 10 visits:
For General Admission, the cost per visit remains at $25 per visit.
Total cost for 10 visits: $25 x 10 = $250
For the Annual Public Session Pass, the cost remains the same at $299, regardless of the number of visits.
Therefore, after 10 visits, it would still be more cost-effective to have the Annual Public Session Pass as the cost per person would still be $299.
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The following question may be like this:
When is it better to have a session pass versus just paying general admission? After 8 visits: How much would each person pay? Show your work for calculations. Session Pass______? General Admission______?After 10 visits: How much would each person pay? Show your work for calculations.Session pass _____? General Admission_____?
GENERAL ADMISSION WITH SKATE RENTAL $25
ANNUAL PUBLIC SESSION PASS WITH SKATE RENTAL $299
LOCKER RENTAL-ONE TIME USE $5
HELMET RENTAL $5
SKATE HELPER-PER HOUR $15
determine the value of x
Answer:
x = 11.62
Step-by-step explanation:
opp / adj would be tangent, so the equation would be 4*tan(71) giving us 11.616, and rounding to the nearest hundredth gives you 11.62
Hope this helps :)
Using a t-distribution table or software or a calculator, report the t-statistic which is multiplied by the standard error to form the margin of error for the following cases: a. 90% confidence interval for a mean with 8 observations. b. 90% confidence interval for a mean with 18 observations. c. 99% confidence interval for a mean with 18 observations.
a. The t-value is 1.895.
b. The t-value is 1.734.
c. The t-value is 2.898.
To calculate the t-statistic for a confidence interval, we first need to determine the degrees of freedom (df), which depends on the sample size minus one. We can then use a t-distribution table, software, or calculator to find the t-value at the desired confidence level and degrees of freedom.
a. For a 90% confidence interval with 8 observations, the degrees of freedom is 7. Using the t-distribution table or calculator,
b. For a 90% confidence interval with 18 observations, the degrees of freedom is 17. Using the t-distribution table or calculator,
c. For a 99% confidence interval with 18 observations, the degrees of freedom is 17. Using the t-distribution table, software, or calculator,
Note that as the sample size increases, the degrees of freedom increase and the t-value approaches the value of the standard normal distribution for large sample sizes. This means that for large sample sizes, we can use the z-value instead of the t-value in confidence interval calculations.
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1. Replacement value: $270,000; coverage 80%
The insurance policy would cover up to $216,000 for the item or property.
If the replacement value of an item or property is $270,000 and your insurance policy provides coverage for 80% of the replacement value, it means that your insurance policy will cover up to 80% of the $270,000 in the event of a covered loss.
To calculate the coverage amount, you would multiply the replacement value by the coverage percentage:
Coverage Amount = Replacement Value * Coverage Percentage
In this case:
Coverage Amount = $270,000 * 0.80
Coverage Amount = $216,000
Therefore, your insurance policy would cover up to $216,000 for the item or property in question. Any losses exceeding this coverage amount would not be covered by your insurance policy.
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Michelle has $15 and wants to buy a combination of dog food to feed at least four dogs at the animal shelter. A serving of dry food costs $1, and a serving of wet food costs $5.
1, Write the system of inequalities that models this scenario
2, Describe the graph of the system of inequality’s including shading and the types of lines graphed. Provide a description of the solution set.
Answer:
Step-by-step explanation:
1. The system of inequalities that models this scenario can be represented as:
Let x be the number of servings of dry food.
Let y be the number of servings of wet food.
The cost constraint:
1x + 5y ≤ 15
The minimum number of dogs constraint:
x + y ≥ 4
2. The graph of the system of inequalities would be a shaded region in the coordinate plane.
To graph the inequality 1x + 5y ≤ 15, we can first graph the equation 1x + 5y = 15 (the corresponding boundary line) by finding two points on the line and connecting them. For example, when x = 0, y = 3, and when y = 0, x = 15. Plotting these points and drawing a line through them will represent the equation 1x + 5y = 15.
Next, we need to shade the region below the line because the inequality is less than or equal to (≤). This shaded region represents the solutions that satisfy the cost constraint.
To graph the inequality x + y ≥ 4, we can again find two points on the line x + y = 4 (the corresponding boundary line). For example, when x = 0, y = 4, and when y = 0, x = 4. Plotting these points and drawing a line through them will represent the equation x + y = 4.
Lastly, we shade the region above the line x + y = 4 because the inequality is greater than or equal to (≥). This shaded region represents the solutions that satisfy the minimum number of dogs constraint.
The solution set is the overlapping region where the shaded areas of both inequalities intersect. This region represents the combination of servings of dry food and wet food that Michelle can purchase within her budget ($15) to feed at least four dogs at the animal shelter.
The inequalities D + W > 4 and D + 5W ≤ 15 model the problem. The graph represents these inequalities, with the overlap of shaded regions showing possible food serving combinations.
Explanation:
Let's define D as the number of servings of dry food and W as the number of servings of wet food. The system of inequalities that models this scenario is:
D + W > 4: Michelle needs enough food for at least four dogs.D + 5W ≤ 15: Michelle cannot spend more than $15.The graph will show the solution sets to the inequalities. D and W must both be non-negative, hence the graphed area is in the first quadrant. The first inequality requires shading above a line that connects (0,4) and (4,0). This line is solid since numbers equal to 4 are included. The second inequality requires shading below a line that connects (0,3) and (15,0). This is also a solid line because Michelle can spend exactly $15. The overlapping region of the graph is the solution set, quantifying the combinations of dry and wet food servings that Michelle can buy.
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Triangle 1 undergoes four different transformations. The results of these transformations are shown. Which statement best describes one of these transformations?
One of the transformations undergone by Triangle 1 is a rotation, which involves turning the triangle around a fixed point while preserving its shape and size.
A rotation is a transformation that turns an object around a fixed point, known as the center of rotation. In the given results, if the triangle appears in a different orientation but retains its shape and size, it indicates a rotation.
During a rotation, each point of the triangle is moved along a circular path around the center of rotation. The distance from the center of rotation remains constant, and the angle between any two corresponding points on the original and rotated triangles is preserved. The direction of rotation can be clockwise or counterclockwise, depending on the given results.
To describe a rotation, we need to specify the angle of rotation and the direction. For example, "Triangle 1 underwent a counterclockwise rotation of 90 degrees" would indicate that the triangle was rotated by 90 degrees in the counterclockwise direction.
The specific rotation can be described by stating the angle of rotation and the direction.
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A normal distribution has a mean of 7 and a standard deviation of 2 . What percent of values are from 7 to 13?
49.87 because I searched it up
NO LINKS!! URGENT HELP PLEASE!!
28. You are skiing on a mountain with an altitude of 1000 feet. The angle of depression is 19°. Find the distance you ski down the mountain. Draw a diagram to represent the situation. Round final answer to the nearest tenth.
Answer:
3071.6 ft
Step-by-step explanation:
In this situation,
We can use sine law,
in which Sin angle = opposite side/ hypotenuse
Similarly
In triangle ABC
SIn A=BC/AC
Sin 19°=1000/AC
Doing criss cross multiplication:
AC= 1000/(Sin 19°)
AC=3071.55 ft
Therefore, the distance I ski down the mountain is 3071.6 ft
The diagram is below.
==============================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(19) = 1000/x
xsin(19) = 1000
x = 1000/sin(19)
x = 3071.553487
x = 3071.6
Refer to the diagram below.
Note that the angle of depression ACD is equal to the angle of elevation BAC because of the alternate interior angles theorem.
When the sun’s angle of depression is 36 degrees, a building casts a shadow of 44 m. To the nearest meter, how high is the building? Enter a number answer only.
The height of the building is approximately 32 meters.
To determine the height of the building, we can use the tangent function, which relates the angle of depression to the height and the length of the shadow.
Let's denote the height of the building as h.
Given that the angle of depression is 36 degrees and the length of the shadow is 44 m, we can set up the following trigonometric equation:
tan(36°) = h / 44
Now, we can solve for h by multiplying both sides of the equation by 44:
h = 44 * tan(36°)
Using a calculator, we find that tan(36°) is approximately 0.7265.
Substituting the value, we get:
h = 44 * 0.7265
Calculating the value, we find:
h ≈ 32 meters
Consequently, the building stands about 32 metres tall.
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