The larger of two numbers is 15 more than the smaller number. If the sum of the two numbers is 27, find the two numbers.
Larger Number:
Smaller Number:
Answer:
Larger number: 21
Smaller number: 6
Step-by-step explanation:
Step 1: Make equations.
x ... larger number
y ... smaller number
First equation: The larger of two numbers is 15 more than the smaller number.
x = y + 15
Second equation: Sum of the two numbers is 27.
x + y = 27
Step 2: Solve the system of equations.
First equation: x = y + 15
Second equation: x + y = 27
Substitute x in second equation with x from first.
x + y = 27
(y + 15) + y = 27
Solve for y.
y + 15 + y = 27
2y = 27 - 15
2y = 12
y = 6
Substitute the calculated value of y back in first equation to get x.
x = y + 15
x = 6 + 15
x = 21
Consider the following cumulative probability distribution.
1 2 3
4
0.09 0.31 0.48 0.65 0.84
5
1
a. calculate a{xs 4). (round your answer to 2 decimal places.)
pox s 4)
p
b. calculate p{x= 3). (round your answer to 2 decimal places.)
p(x = 3)
#
+
e
10
19
34
m
c. calculate p(2 s x s 4). (round your answer to 2 decimal places.)
p(2 5 x 84)
The solution [tex]P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)[/tex] is mathematically given as
[tex]P(2 \leq X \leq 4)=0.84[/tex]P(X=3)= 0.17[tex]P(2 < =X\leq 4)=0.53[/tex]What is the solution [tex]P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)[/tex]?Generally, the equation for the Probability of P(X=3) is mathematically given as
b)
[tex]P(X=3) = P(X \leq 3)-P(X\leq 2)[/tex]
Therefore
[tex]P(X=3)= 0.65-0.48[/tex]
P(X=3)= 0.17
c)
[tex]P(2\leq X\leq 4) = P(X\leq 4)-P(X\leq 1)\\\\\\P(2\leq X\leq 4) = 0.84-0.31'[/tex]
[tex]P(2 < =X\leq 4)=0.53[/tex]
a)
[tex]P(2\leq X\leq 4)=0.84[/tex]
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After arguing for two weeks, melissa convinced her parents to have her birthday party at flyzone trampoline park. as soon as she gets there, melissa spends time practicing flips on the trampolines. then, she spends 1/2 of an hour eating birthday cake with her friends. in all, melissa spends 1/4 hours at flyzone.
The amount of time that Nora practices flips is; t = 1 ¹/₄
How to Solve Algebra problems?We are told that;
Nora spends time practicing flips on the trampolines. Let this be t.
Then, she spends 1/2 of an hour eating birthday cake with her friends.
Thus, total amount of time spent on flips and eating with her friends is;
t + ¹/₂ = 1 ³/₄
t = 1 ³/₄ - ¹/₂
t = 1 ¹/₄
Complete Question is;
After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?
Solve this equation for (t) to find the amount of time Nora practices flips
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calculate the area of this triangle :
b = 12cm
h = 5cm
side = 13cm
I NEED THE ANSWER ASAP !!
Applying it's formula, the area of the given triangle is of 30 centimeters squared, that is, 30 cm².
What is the area of a triangle?The area of a triangle of base b and height h is given by half the multiplication of these measures, that is:
A = 0.5bh.
In this problem, we have that b = 12 cm, h = 5 cm, hence:
A = 0.5 x 12 cm x 5 cm = 30 cm².
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Prove: Every point on the perpendicular bisector of a segment is equidistant from the ends of the segment.
Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Two boxes of apples weigh 35 lb. If one of the boxes weighs 12 lb, then find the weight of the second box.
PLEASE HELP ILL MAKE YOU THE BRAINIEST
Answer:
yes . because the given number satisfy the equation a2+b2=c2
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ (30)^{2} + (40)^{2} = (50)^{2} \\ 900 + 1600 = 2500 \\ 2500 = 2500 [/tex]
Yes. because the given numbers do satisfy the equation a²+b²=c².
What is the equation of the line that is perpendicular to y = 2x + 9 and has a y-intercept of –3?
Answer:
The image has the ans.
Step-by-step explanation:
Image explains.
Which image is a reflection of the orange letter K in Quadrant I?
I'll give you brainliest if you actually answer my question
The answer is the green K in quadrant IV
what is the Cartesian co-ordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.
Given here: The K in the fourth quadrant is a reflection of K in the first quadrant because it first flips the K and but there is no change in the position of the x-axis quite clearly.
Hence, The answer is the green K in quadrant IV
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Select the correct answer.
Which equation is equivalent to the given equation?
- 4(x - 5) + 8x = 9x - 3
A.
-5x = -23
B.
5x = 17
C.
-5x = 2
D.
5x = -12
Answer:
A. -5x = -23
Step-by-step explanation:
First you have to simplify the equation - 4(x - 5) + 8x = 9x - 3
-4x + 20 + 8x = 9x -3
9x - 4x = 20 + 3
5x = 23
=> equivalent to answer A.
The equivalent expression is,
⇒ - 5x = - 23
We have to given that,
An expression is,
- 4 (x - 5) + 8x = 9x - 3
Now, We can simplify the expression for equivalent expression,
- 4 (x - 5) + 8x = 9x - 3
Apply distributive property, we get;
- 4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
4x - 9x = - 20 - 3
- 5x = - 23
Therefore, The equivalent expression is,
⇒ - 5x = - 23
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jennifer invests $2,302 in a money market account. the account pays 2.1% simple interest annually. if she doesn’t add or subtract any money, is it reasonable to expect that jennifer will earn about $200 in simple interest in 5 years?
Jennifer would earn more than $200. She would earn $230.02 over the period.
What is the simple interest that Jennifer would earn?Simple interest is a type of interest paid only on the money invested.
Simple interest = amount invested x interest rate x time
2302 x 5 x 0.021 = $230.20
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y2-y1
m =
X2-X1
Find the slope of the line that passes
through these two points.
Simplify completely.
(1,5)
(4,6)
m =
[?]
Answer:
[tex]\sf m=\dfrac{1}{3}[/tex]
Step-by-step explanation:
The slope of a line can be found using the following formula:
[tex]\sf m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Given the points (1, 5) and (4, 6):
where:
x₁ = 1, x₂ = 4
y₁ = 5, y₂ = 6
Substitute these values into the formula:
[tex]\sf \sf m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{6-5}{4-1}\\\\m=\dfrac{1}{3}[/tex]
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I need help bad I dont understand this
Answer:
12.566 inches
Step-by-step explanation:
2πr/4
2π x8 divided by 4
Problem Solving
Nicholas is 32 years older than Martina. 9 years ago the sum of their ages was 56. How old is each now?
Answer:
make variables and solve with A
that's the song pota pota pota
Step-by-step explanation:
Answer:
I believe your answer is Nicholas is 53 and Martina is 21
Step-by-step explanation:
44+12=56
9 years later
53 and 21
Which equation matches the graph of the greatest integer function given
below?
A. y = [x]-2
B. y = [x] +2
C. y -[x]+3
D. y = [x]-3
The equation that matches the graph of the greatest integer function is y = [x] - 2
How to determine the equation?The parent function of an step function is represented as:
y = [x]
From the given graph, we can see that the lines are shifted 2 units down.
This means that:
(x,y) = (x,y - 2)
So, we have:
y = [x] - 2
Hence, the equation that matches the graph of the greatest integer function is y = [x] - 2
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An economist wanted to investigate the relationship between office rents (the dependent variable) and vacancy rates. Accordingly, he took a random sample of monthly office rents and the percentage of vacant office space in 30 different cities. a. Determine the regression line. b. Interpret the coefficients.
The regression line will be y = 20.64 - 0.3038x.
How to explain the regression?It should be noted that regression is a statistical method that determine the relationship between the variables.
Here, the regression line will be y = 20.64 - 0.3038x. The slope coefficient is -0.03038 and the intercept is 20.460.
The slope coefficient defines that for a unit increase in the percentage of vacancy rate will reduce 0.3038 unit of monthly office rent.
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ABC Car Share Inc. offers car sharing for a $199 yearly fee plus $14/hr for the
use of its car share. What is the total cost for a person who purchases a car
share and uses it for 72 hours total time?
OA. $1307
OB. $1107
C. $1207
OD.
$1407
SUBMIT
Answer:
C
Step-by-step explanation:
199+(14*72) = 1207
annual fee plus cost for each hour used
Ii
a survey asked 6,000 random college students about how they are paying for college.
one thousand students surveyed responded that they have taken out student loans.
which conclusion can be made about the population from this survey?
o a. most college students do not use students loans.
o b. half of college students are using students loans.
oc. one-quarter of college students are using students loans.
od. all college students are using students loans.
Answer:
Answer = most college students do not use students loans.
Step-by-step explanation:
To find the percentage of students taking out student loans we take 1,000/6000 to get roughly 17%. This is a very small number of students taking out student loans.
A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting an insect?
Express the probability as a reduced fraction
Answer:
1/3
Step-by-step explanation:
[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
*WILL GIVE BRAINLIEST* The table below contains partial data points of Red Bird's trajectory.
Horizontal distance traveled is 12unit, Equation in standard form is y = -4x² + 120x - 680 and Equation in vertex form is y = -4(x - 15)² + 220
Horizontal Distance Traveled
To find the horizontal distance traveled by Red Bird, we need to calculate the difference between the largest and smallest values of the X-axis data points. In this case, the horizontal distance traveled is:
Horizontal Distance Traveled = Largest X value - Smallest X value
= 17 - 5
= 12 units
The horizontal distance traveled by Red Bird is 12 units.
Equation in Standard Form
To find the equation in standard form, we need to determine the equation of a quadratic function that fits the given data points. Since we have more than three data points, we can use a quadratic regression to find the equation.
Using a regression tool or mathematical software, the equation in standard form for the given data points is:
y = -4x² + 120x - 680
Equation in Vertex Form
To find the equation in vertex form, we can convert the equation from standard form to vertex form by completing the square. The vertex form of a quadratic equation is given by:
y = a(x - h)² + k
To convert the equation to vertex form, we need to rewrite it by completing the square. The steps are as follows:
y = -4x² + 120x - 680
First, factor out the common coefficient -4:
y = -4(x² - 30x + 170)
To complete the square, we need to add and subtract the square of half the coefficient of x, which is (30/2)² = 225:
y = -4(x² - 30x + 225 - 225 + 170)
Now, rewrite the equation by grouping:
y = -4((x - 15)² - 55)
y = -4(x - 15)² + 220
The equation in vertex form is:
y = -4(x - 15)² + 220
So, the equation in vertex form for the given data points is y = -4(x - 15)² + 220.
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Danny attempted to complete a 500 piece puzzle. By the end of the night, he places p pieces in the puzzle correctly, which expression shows how many more pieces he needs to add to the puzzle to complete it
The expression that shows how many more pieces he needs to add to the puzzle to complete it is 500 - p
How to determine the expression?The given parameters are:
Total = 500
Correct = p
The remaining piece is calculated using:
Total =Correct + Remaining
Substitute known values
p + Remaining = 500
Subtract p from both sides
Remaining = 500 - p
Hence, the expression is 500 - p
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HURRY please answer this
Which expression is represented by the model?
While traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent.while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent. 1 european euro = 1.3687 us dollars
Answer:
$44.69
Step-by-step explanation:
150 x 1.3687 = $205.305 = $205.31
250 - 205.31 = $44.69
(Hope this helps ^-^)
Answer
44.70 US dollars
Step-by-step explanation: Edg right? If thats what youre reffering too then this is correct
Joseph and his children went into a movie theater where they sell bags of popcorn for $7.50 each and pretzels for $4.75 each. Joseph has $95 to spend and must buy no less than 16 bags of popcorn and pretzels altogether. If
x
x represents the number of bags of popcorn purchased and
y
y represents the number of pretzels purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
Step-by-step explanation:
In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each represents.
The slope of the graph is 745 and the y-intercept of the graph is 500
How to determine the slope?The points are given as:
(2, 1990) (5, 4225) (9, 7205)
The slope is calculated using:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (4225 - 1990)/(5 - 2)
Evaluate
m = 745
This means that the amount earned per day is 745
Hence, the slope of the graph is 745
How to determine the y-intercept?In (a), we have
m = 745
To calculate the y-intercept, we use the following points
(x1 , y1) = (0,y)
Recall that:
m = (y2 - y1)/(x2 - x1)
So, we have:
745 = (4225 - y)/(5 - 0)
Evaluate the difference
745 = (4225 - y)/(5)
Multiply both sides by 5
3725 = 4225 - y
Solve for y
y = 500
This means that the initial amount earned is 745
Hence, the y-intercept of the graph is 500
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Simplify this expression.
(2-5√6)-3√2
A. 6√2-15√6
B. 6√2-15√12
C. 6√2-8√6
D. 6√2-30√3
Answer:
-A.
Step-by-step explanation:
/Correct Me If I'm Not Correct/
"Hope it's Help"
Given: ΔABC (to the right)
AB=15
BD=9
AD⊥BC
m∠C=30°
Find Perimeter of ABC
Applying the Pythagorean theorem and the trigonometric ratios, the perimeter of triangle ABC is: 68.8 units.
What is the Perimeter of a Triangle?The perimeter of a triangle = sum of its 3 sides.
Given the following:
AB = 15 BD = 9m∠C=30°Use the Pythagorean theorem to find AD considering triangle ADB as a right triangle:
AD = √(15² - 9²)
AD = 12 units
Use the trigonometric ratios to find DC and AC:
sin 30 = AD/AC
sin 30 = 12/AC
AC = 12/sin 30
AC = 24 units
tan 30 = AD/DC
tan 30 = 12/DC
DC = 12/tan 30
DC ≈ 20.8 units
BC = BD + DC = 9 + 20.8
BC = 29.8 units.
Perimeter of triangle ABC = BC + AB + AC
Perimeter of triangle ABC = 29.8 + 15 + 24
Perimeter of triangle ABC = 68.8 units.
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Solve the equation 9x2 + 8x - 5= 3x² to the nearest tenth
Answer:
x=13
Step-by-step explanation:
9*2+8x-5=3x^2
9*2 = 18
18-5=13
13+8x=3x^2
3x^2 = 9x
13+8x=9x
-8x -9x
13=x
x=13
Please help!! Simplify fully:
Answer:
[tex]9 {e}^{6 } [/tex]
Step-by-step explanation:
yes
4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received.
How many slices of pizza did Harris eat?