Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.
As given,
Given interval:
( -4 , -1 )
Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).
Given interval ( -4 , -1 ) is open interval.In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.-4 and -1 are exclusive values for the given variable.Symbol representing open interval is sign of < or >.Interval (-4,-1) in inequality notation is given by -4 < x < -1.All values are included between -4 and -1 except -4 and -1.Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.
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Let p: The shape is a rhombus.
Let q: The diagonals are perpendicular.
Let r: The sides are congruent.
Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?
p ∧ (q ∧ r)
(p ∨ q) ∨ r
p ↔ (q ∧ r)
(p ∨ q) ↔ r
The correct representation of statement ''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent'' will be;
⇒ p ↔ (q ∧ r).
What is Logic operators?
A symbol or words to use to connect two or more expressions are called Logic operators.
Given that;
The statement is,
''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent''
Now,
Since, The word ''if and only if'' is represent by using the biconditional logic operator (↔) and the word ''and'' is represented by using the logical conjunction operator (∧).
So, The logic representation of the statement;
"The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent” will be;
⇒ p ↔ (q ∧ r).
Thus, The correct representation of statement ''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent'' will be;
⇒ p ↔ (q ∧ r).
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A falling object travels a distance given by the formula d = 4t + 6t?, where d is measured in feet and t is measured in seconds.
How many seconds will it take for the object to travel 68 feet? Round the answer to 4 decimal places.
If a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds
The formula of the object traveling a distance d = 4t + [tex]6t^{2}[/tex]
Where d is the distance traveled in feet
t is the time taken in seconds
Here
The distance traveled = 68 feet
Therefore the equation will be
68 = 4t + [tex]6t^{2}[/tex]
[tex]6t^{2} +4t-68=0[/tex]
We have to solve quadratic equation [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
a = 6
b = 4
c = -68
Substitute the values in the equation
= [tex]\frac{-4+/-\sqrt{4^2-(4)(6)(-68)} }{(2)(6)}[/tex]
= [tex]\frac{-4+/-\sqrt{1648} }{12}[/tex]
t = [tex]\frac{-1+/-\sqrt{103} }{3}[/tex]
We take only positive value
t = [tex]\frac{-1+\sqrt{103} }{3}[/tex]
t = 3.0496 seconds
Hence, if a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds
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The sum is the measure of three angles of a triangle is 180 degrees. In a triangle, the measures of an angle are x,x+12 and x-48. What is the measure of each angle?
Answer:
24° , 72° , 84°
Step-by-step explanation:
sum the 3 angles and equate to 180 , that is
x + x + 12 + x - 48 = 180
3x - 36 = 180 ( add 36 to both sides )
3x = 216 ( divide both sides by 3 )
x = 72
Then the measure of the 3 angles are
x = 72°
x + 12 = 72 + 12 = 84°
x - 48 = 72 - 48 = 24°
The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:98.9 96.6 98.6 99.7 97 97.4 99.4Assume body temperatures of adults are normally distributed. Based on this data, find the 98% confidenceinterval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e.,parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.98% C.I. -
Given the data temperatures to be;
[tex]98.9,96.6,98.6,99.7,97,97.4,99.4[/tex]We would require the following to get the 98% confidence interval of the mean body temperature.
Mean, Standard deviation, sample size, Probability of a confidence interval of 98%.
Using a calculator, we can get the mean to be
[tex]\text{(}\mu)=98.2285[/tex]The standard deviation would be derived to be;
[tex]\sigma=1.2230[/tex]The sample size can be gotten from the question to be;
[tex]n=7[/tex]The probability value of a 98% confidence interval is given to be 2.33
We can then derive the answer using the formula below;
[tex]\mu\pm z^x(\frac{\sigma}{\sqrt[]{n}})[/tex]We would substitute into the formula
[tex]\begin{gathered} \mu\pm z^x(\frac{\sigma}{\sqrt[]{n}}) \\ =98.2285+2.33(\frac{1.2230}{\sqrt[]{7}}) \\ =98.2285\pm1.0770 \\ =(97.152,99.306) \end{gathered}[/tex]ANSWER:
[tex](97.152,99.306)[/tex]Please help me solve and show the steps so I could understand
Given polygon with sides 8 and radius 10yd.
Formula for area of ploygon
[tex]=n\times r^2\times tan\left(\frac{\pi}{n}\right)[/tex]So, solving further
[tex]\begin{gathered} =8\times10^2\times tan(\frac{\pi}{8}) \\ =800\times0.414 \\ =331.37 \end{gathered}[/tex]Hence, 331.37 yd square is the area of polygon.
P(6, -3); y = x + 2
Write an equation for the line in point-slope form.
The equation of the line by using slope value is: y = x -9
What is slope of a line?
The slope of a line explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the slope value, it is classified as whether lines are parallel or perpendicular.
According to the question, the given parameters for the line segment is as written below:
Equation of a line = x + 2 and the coordinate points = (6, -3): (x = 6; y = -3)
Now, by using standard equation for the line segment: y = mx + c
where, 'm' is the slope; c is the y-intercept; (x, y) are coordinates
Substituting given values that is slope and y-intercept in the standard equation, we get:
y = mx + c
⇒ -3 = (1)(6) + c
⇒ c = -3 - 6 = -9
Therefore, the value of the y-intercept is: c = (-9)
equation of the line by substituting the value of the y-intercept as well as slope value:
y = (1)x + (-9) = y = x -9
Hence, the equation of the line by using slope value is: y = x -9
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Which equation is the correct translation of the following statement?Four less than a number is nine.9 - x = 49 - 4 = xx - 4 = 94 - x = 9
Given
The statement,
Four less than a number is nine.
To find:
Which equation is the correct translation of the following statement?
Explanation:
Let x be the number.
Since four less than a number is nine.
Then,
[tex]x-4=9[/tex]Hence, the correct statement is x-4=9.
On the graph below, which dotted line represents a reflection across the x-axis of the red-solid-line graph?5 stars for quicknessplease look at png 1 is question 2 is answer
Hello!
The rule for a reflection across the x-axis is:
[tex](x,y)=(x,-y)[/tex]Knowing it, let's write some points that the red line passes through:
(-2, 0) and (0, 4).
Now, let's use this rule and change the sign of the y coordinate:
• (-2, 0) → (-2, 0) because +0 or -0 doesn't exist.
,• (0, 4) → (0, -4)
Let's analyze it and find a line that passes through these two points:
(-2, 0) and (0, -4)
It will be the blue line.
Use a model to divide. 2/5÷4 Express the answer in simplest terms.
so the equation si:
[tex]\frac{\frac{2}{5}}{4}[/tex]This is equal to:
[tex]\frac{2}{20}=\frac{1}{10}[/tex]Finally:
[tex]\frac{1}{10}=0.1[/tex]Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)
Answer: its not correct because the got different perenties or groupings and they mean different meaning
Step-by-step explanation:
you and three friends share a sushi boat at House of Kobe the cost of the boat is $50 you each also pay for a soft drink that is $2.39 what is the total cost of the meal after you pay 6% tax
ANSWER
$63.13
EXPLANATION
We have that the cost of the boat is $50.
Each of you and your friends (that is four of you) will pay for a soft drink that cost $2.39 each.
The cost of the soft drinks will therefore be:
4 * 2.39 = $9.56
Adding the cost of the boat, total cost will be:
$9.56 + $50 = $59.56
Now, we have to add a tax of 6%, so we find 6% of total cost:
[tex]\frac{6}{100}\cdot\text{ 59.56 = \$3.57}[/tex]Finally, add the tax to the cost:
$59.56 + $3.57
= $63.13
You pay a total of $63.13 (including tax)
I need help please 5. Find the distance between C (-5, 4) and Q (2,0). A. 22 B. 33 C. 53 D. 65
Given the two points:
C (-5, 4) and Q (2, 0)
To find the distance, use the distance formula below:
[tex]d\text{ =}\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where,
(x1, y1) = (-5, 4)
(x2, y2) = (2, 0)
Therefore, we have:
[tex]\begin{gathered} d=\sqrt[]{(2-(-5))^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{(2+5)^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{7^2+(-4)^2} \\ \\ \text{ =}\sqrt[]{49+16} \\ \\ \text{ =}\sqrt[]{65} \end{gathered}[/tex][tex]undefined[/tex]Solve this inequality for the y variable: 6x-9y> 12 u y GON 4 3 2 4 O ya 3 2. 4 ys vs - 2 x + 2
We solve the inequality as follows:
[tex]6x-9y>12\Rightarrow-9y>-6x+12[/tex][tex]\Rightarrow y<\frac{2}{3}x-\frac{4}{3}[/tex]Jae created a painting with an area of 48 square inches and a length of 6 inches. They create a second painting with an area of 64 square inches. It has the same width as the first painting. What is the length of the second painting?
An item is regularly priced at $50. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?Amount discounted: sX5?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
regular price = $50
discount = 40% = 0.4
Step 02:
amount discounted:
amount discounted = regular price * discount
amount discounted = $50 * 0.4 = $20
The answer is:
$20
1. The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?
To find the probability for the number who tested positive we divide the positive cases between the total of the covid tests and then mutiply by 100.
P = (8,533/68,811)* 100
P = 12.400, the nearest hundredth of a percent is 12.
11690000 people who live in ohio and the testing results is that 12% of this people would test positive for the virus. so we need to find percentage 12 for 11690000.
(11690000* 12) / 100
1402800 is the number of people who would test positive for the virus
The area of a triangle is given by A = 1/2bh, where b is the base and h is the height of the triangle
The area of the triangle with base 12 units, and height of 3 units is: B. 18.
How to Determine the Area of a Triangle?To find the area of a triangle, find the height, which is the distance from its base to its highest point, and also find the length of the base of the triangle, then apply the formula below:
Area of triangle = 1/2 × base × height
From the information given, the following are the parameters we will need to work with:
Base of the triangle = QR = 12 units
Height of the triangle = PH = 3 units
Plug in the values
Area of triangle = 1/2 × 12 × 3
Area of triangle = 36/3
Area of triangle = 18 units
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Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.6x48x556x47
The question asks us to confirm the simplification of the expression:
[tex]-\frac{48x^5}{56x^4}[/tex]Step 1: Factor the numbers
[tex]\begin{gathered} 48=8\times6 \\ 56=8\times7 \end{gathered}[/tex]Therefore, the expression becomes:
[tex]-\frac{48x^5}{56x^4}=-\frac{8\times6x^5}{8\times7x^4}[/tex]Step 2: Cancel out the common terms from the expression
[tex]-\frac{8\times6x^5}{8\times7x^4}=-\frac{6x^5}{7x^4}[/tex]Step 3: Apply the rule of exponents
[tex]\frac{x^n}{x^n}=x^{m-n}[/tex]Therefore, we have:
[tex]-\frac{6x^5}{7x^4}=\frac{6}{7}x^{5-4}=-\frac{6x}{7}[/tex]CONCLUSION
The expression simplifies to give:
[tex]-\frac{48x^5}{56x^4}=-\frac{6x}{7}[/tex]The answer is TRUE.
2. Zandile invests her Christmas bonus for R 875.00 in a bank that offers
interest rates of 9% p.a. compounded half-yearly. How much interest will she
have earned after 6 years? I want the interest
After 6 years, Zandile earns an interest of rupees 608.9 after investing her Christmas bonus for R 875.00 in a bank that offers interest rates of 9% p.a. compounded half-yearly.
What is interest?The simplest way to calculate interest is as a percentage of the principal. For instance, if you agreed to borrow $100 from a friend with 5% interest, the interest you would pay would only be 5% of $100: $100(0.05) = $5.
What is compound interest?Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The principal (original) sum and the interest that has already accrued over the course of previous periods are used to calculate compound interest.
Here,
Principal amount= 875
Rate of interest= 9% pa
Compounding= half-yearly (2/year)
Time= 6 years
A = P(1 + r/n)ⁿᵇ
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
b=number of time periods elapsed
A=875(1+9/6)⁶*²
A=₹1,483.90
Zandile invests her Christmas bonus of R 875.00 in a bank that offers interest rates of 9% per year compounded semi-annually, and after 6 years, she earns an interest of Rs 608.99.
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find 11/3÷2/3
The quotient is 5 and ___.
After conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.
What are mathematical operations?A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count. A mathematical operation is a procedure. A mathematical operation can be anything from addition to subtraction to multiplication to division to finding the root.So, 11/3÷2/3:
We need to perform the division of the given fractions as follows:(Refer to the image attached below for calculations)11/3÷2/3 = 5½Therefore, after conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.
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Factor: x^6-5x^4-5+x
The value of the expression x^6 -5x^4 - 5 + x when simplified is x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as
Factor: x^6 -5x^4 - 5 + x
From the above expression, we have
x^6 -5x^4 - 5 + x
Group the expression in two'2
So, we have
x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)
Factorize each group of the expression
So, we have
x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)
The above expression cannot be further simplified
Hence, the value of x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)
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Which equation demonstrates the distributive property? Responses A 36 + 9 = 4536 + 9 = 45 B 36 + 9 = 3(12 + 3)36 + 9 = 3(12 + 3) C 36 x 9 = 9 x 3636 x 9 = 9 x 36 D (12 + 3)3 = 3(12 + 3)
The correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.
What is distributive property ?
Distributive property states that the outcomes are the same whether the numbers in parenthesis are added before or after multiplication.
We know that according to the distributive property both sides must be equal such that the outcomes are same whether the numbers in parenthesis are added before or after multiplication. The expression for distributive property is given as : a(b + c) = ab + ac
So , checking the options one by one :
A) 36 + 9 = 45 ; is not an equation representing distributive property as it doesn't satisfy the criteria of a distributive property.
B) 36 + 9 = 3(12 + 3) is an equation representing distributive property as it satisfies the criteria mentioned above i.e.,
36 + 9 = 3 × 12 + 3 × 3
36 + 9 = 36 + 9
45 = 45
C) 36 x 9 = 9 x 36 is not an equation representing distributive property.
D) (12 + 3) × 3 = 3 × (12 + 3) is not an equation representing distributive property because both sides are written in the same way.
Therefore , correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.
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Explain how you can use an array to find partial products for 4x36.
Answer:
(4 x 30) +(4 x6)
120 + 24
144
Step-by-step explanation:
Please help me solve: Part CA sign in a freight elevator states that the maximum capacity of the elevator is 2,500 pounds. Use the average weight of a box as 75 pounds and the average weight of a crate as 160 pounds to complete the following parts.If there are 13 average-weight boxes on the elevator, what is the maximum number of average-weight crates that can also be on the elevator given its maximum capacity? Please explain.
Let
x ----> number of average-weight crates
so
we have that
[tex]75(13)+160x\leq2,500[/tex]solve for x
[tex]\begin{gathered} 975+160x\leq2,500 \\ 160x\leq2,500-975 \\ 160x\leq1,525 \\ x\leq9.53 \end{gathered}[/tex]therefore
the maximum number of average-weight crates is 9Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²
The given equation is:
[tex]y=\frac{5}{x^2}[/tex]a. Find the value of dy/dx when x=3
Start by finding the derivative:
[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):
[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:
[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:
[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:
[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]b. Estimate the value of 5/(2.98)^2:
[tex]\begin{gathered} y=\frac{5}{x^2}=\frac{5}{2.98^2}=0.563 \\ \text{Which also means x=2.98} \\ \text{Let's find the derivative when x=2.98} \\ \frac{dy}{dx}=\frac{-10}{2.98^3}=\frac{-10}{26.46}=-0.377 \end{gathered}[/tex]Find the x-intercept and y- intercept of the function f(x) = (2x + 3)/(x ^ 2 + 3)can u draw the function of f(x) = (2x + 3)/(x ^ 2 + 3)?Need solution ^^
Answer:
• x-intercept: (-1.5, 0).
,• y-intercept: (0, 1).
Explanation:
Given the function:
[tex]f(x)=\frac{2x+3}{x^2+3}[/tex](a)x-intercept
The x-intercept is the value of x at which f(x)=0.
When f(x)=0
[tex]\begin{gathered} \frac{2x+3}{x^2+3}=0 \\ \text{ Cross multiply} \\ 2x+3=0 \\ \text{ Subtract 3 from both sides of the equation} \\ 2x+3-3=0-3 \\ 2x=-3 \\ \text{ Divide both sides of the equation by 2} \\ \frac{2x}{2}=-\frac{3}{2} \\ x=-1.5 \end{gathered}[/tex]The x-intercept is located at (-1.5, 0).
(b)y-intercept
The y-intercept is the value of f(x) at which x=0.
When x=0
[tex]\begin{gathered} f(x)=\frac{2x+3}{x^2+3} \\ f(x)=\frac{3}{3} \\ f(x)=1 \end{gathered}[/tex]The y-intercept is at (0, 1).
(c)Graph
The graph of f(x) is given below:
3300 dollars is placed in an account with an annual interest rate of 6.75%. To
the nearest tenth of a year, how long will it take for the account value to reach
10700 dollars?
The simple interest formula is A = P(1+r t) then the value of t =33.2210 years.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The simple interest formula is equal to
A = P(1+r t)
where, A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
P = $ 3300
A = $ 10700
r = 6.75 % = 6.75 / 100 = 0.0675
substitute in the formula above
$10700 = 3300(1+0.0675 t)
simplifying the above equation, we get
Divide both sides by 3300
[tex]$\frac{3300(1+0.0675 t)}{3300}=\frac{10700}{3300}$$[/tex]
Simplifying the above equation, we get
[tex]$1+0.0675 t=\frac{107}{33}$$[/tex]
Subtract 1 from both sides
[tex]$1+0.0675 t-1=\frac{107}{33}-1$$[/tex]
Simplifying the above equation, we get
[tex]$0.0675 t=\frac{74}{33}$$[/tex]
Divide both sides by 0.0675
[tex]$\frac{0.0675 t}{0.0675}=\frac{\frac{74}{33}}{0.0675}[/tex]
[tex]$t=\frac{74}{2.2275}$[/tex]
t = 33.2210 years
Therefore, the value of t exists 33.2210 years.
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If f(x) = 5x + 40, what is f(x) when x = -5?
we have the following:
[tex]f\mleft(x\mright)=5x+40[/tex]replacing, x = -5
[tex]\begin{gathered} f(-5)=5\cdot-5+40 \\ =-25+40 \\ =15 \end{gathered}[/tex]The answer is 15
What kind of transformation converts the graph of f(x) = -x - 10 into the graph of g(x)
-9x - 10?
horizontal stretch
vertical stretch
vertical shrink
horizontal shrink
=
Answer:
zeroay horizontal stretch vertical shrink
Step-by-step explanation:
1+1=2
how would I answer and what would be the answer?
Answer: (-1, 0)
The interval of decreasing refers to the interval of x-values where the graph is decreasing or going down.
If we look at the graph:
We can see that the graph starts to decrease or "go down" at values x = -1 and x=0. With this, we can conclude that the interval of decrease for the given graph is (-1, 0)