7 groups of 2/7 is equivalent to the whole, which is represented by the number 2.
When we have 7 groups of 2/7, we are essentially multiplying the fraction 2/7 by the whole number 7. To perform this operation, we can use the following formula:
a/b × c/d = ac/bd
where a, b, c, and d are any numbers, and a/b and c/d are two fractions.
In our case, a is 2, b is 7, c is 7, and d is 1. This is because we want to multiply 2/7 by 7 to get 7 groups of 2/7. Therefore, we can substitute these values into the formula:
2/7 × 7/1 = (2 × 7) / (7 × 1) = 14/7
The result is a fraction 14/7, which can be simplified to 2. This means that 7 groups of 2/7 is equal to 2. To simplify this further, we can say that if we divide a whole into 7 equal parts, each part is 2/7. If we have 7 of these parts, we have the whole.
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An triangle has vertices
as shown in the diagram. It has been translated vertically and/or horizontally to the triangle with vertices labelled
and
using a translation matrix defined as
.
A coordinate system has an unlabeled horizontal x-axis and an unlabeled vertical y-axis. There are 2 right triangles. The first triangle has vertices labeled A, B and C. Point A is 2 units to the left of the origin, point B is at the origin, and point C is 1 unit above the origin. The second triangle has vertices labeled A’, B’, and C’. Point A’ is 1 unit below the origin. Point B’ is 2 units to the right and one unit below the origin. Point C’ is 2 units right of the origin.
(The choices and pic are attached.)
The translation matrix is,
[tex]\left[\begin{array}{ccc}2&2&2\\-1&-1&-1\end{array}\right][/tex]
How to solveThe coordinates of the triangle as a coordinate matrix is
-2 0 0
0 0 1.
Here the triangle has been translated 2 units right and 1 unit down.
Translating the triangle 2 units to the right means that each x -coordinate increases by 2.
Translating the triangle 1 unit down means that each y -coordinate decreases by 1.
So the translation matrix is,
[tex]\left[\begin{array}{ccc}2&2&2\\-1&-1&-1\end{array}\right][/tex]
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A vending machines coin box contains nickels dimes and quarters the total number of coins in the box is 312 the number of dimes is three times the number of nickels and quarters together and the box contains $31.30 find the number of nickels dimes and quarters that it contains
Answer:
58 nickels; 234 dimes; 20 quarters
Step-by-step explanation:
number of dimes = d
number of nickels = n
number of quarters = q
n + d + q = 312
d = 3(n + q)
0.05n + 0.1d + 0.25q = 31.3
n + d + q = 312
d = 3n + 3q
5n + 10d + 25q = 3130
n + 3n + 3q + q = 312
5n + 30n + 30q + 25q = 3130
4n + 4q = 312
35n + 55q = 3130
n + q = 78
7n + 11q = 626
n = 78 - q
7(78 - q) + 11q = 626
546 - 7q + 11q = 626
4q = 80
q = 20
n = 78 - 20 = 58
d = 3(58 + 20) = 3(78) = 234
Answer: 58 nickels; 234 dimes; 20 quarters
Line, line segment, angle,ray
A population has a mean = 76 and a standard deviation o = 24. Find the mean and standard deviation of a sampling distribution of sample means with sample
size n = 64.
The mean and standard deviation is x ~ N(76,3).
Given that a population has a mean = 76 and a standard deviation o = 24
We need to find the standard deviation of a sampling distribution of sample means with sample, n = 64.
The mean of the sampling distribution of sample means is =
x = μ
x = 76
Now,
SD = σ/√n
= 24/√64
= 24/8
= 3
Hence, x ~ N(76,3).
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Help xangle, x and
∠
y
∠yangle, y are supplementary angles.
∠
y
∠yangle, y measures
14
2
∘
142
∘
142, degrees.
What is the measure of
∠
x
∠xangle
Answer:
∠x = 38°
Step-by-step explanation:
∠x + ∠y = 180°
∠x + 142° = 180°
∠x = 180° - 142
∠x = 38°
#CMIIWfind the value of 6!.
Answer:
the absolute value of 6 is just 6
Solve the following problems using the Charged Chip model. Please draw pictures and explain your thinking for each
problem:
1.9+(-4)
2.9-(-4)
3.-9+4
4.-9-(-4)
5. Make up your own problem and then solve it!
The values with Charged Chip model are
9 + (-4) = 5.
9-(-4)=13
-9+4=-5
-9-(-4)=-5
To solve 9 + (-4), we start with 9 positive chips and take away 4 negative chips. We can represent this as:
[+][+][+][+][+][+][+][+][+]
[-][-][-][-]
When we combine the chips, we end up with 5 positive chips remaining:
[+][+][+][+][+]
Therefore, 9 + (-4) = 5.
To solve 9 - (-4), we start with 9 positive chips and add 4 negative chips. We can represent this as:
[+][+][+][+][+][+][+][+][+]
[-][-][-][-]
When we combine the chips, we end up with 13 positive chips remaining:
[+][+][+][+][+][+][+][+][+][+][+][+][+]
Therefore, 9 - (-4) = 13.
Similarly -9+4 value is -5
-9-(-4) value is -5
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i need help pls will give brainlist
Answer:
the answer is C!
PC.64 Carl's Carpet Cleaning Company is searching for ways to become more productive in its carpet cleaning process. He has invested in new equipment and has also been experimenting with new cleaning solution recipes in order to lower costs and improve quality. Carl plans to iron out all the bugs in his improved process so that he can grow his company by franchising. The table below gives information on the last two months of carpet cleaning jobs with the most recent month showing the results after these changes were made: Outputs / Inputs Price/Cost per Unit ($) Two Months Back Last Month Carpets Cleaned $89 72 85 Labor (hours) $10.50 130 126 Solution (gallons) $6.99 125 102 What was the two-months-ago single-factor productivity for Carl's Carpet Cleaning in terms of labor dollars? In other words, for every dollar spent on labor, how many dollars of sales would they obtain? (Display your answer to two decimal places.) 4.69 From two months ago to last month, by what percentage did Carl's productivity increase or decrease in terms of solution (gallons and number of carpets cleaned, not revenue dollars)? Write your answer as a percentage. Display your answer to two decimal places. 44.68 % What was last month's multi-factor productivity (not two months ago) for Carl's Carpet Cleaning in terms of dollars? (In other words, how many dollars of revenue did each dollar of inputs produce?) (Display your answer to two decimal places.) Number By what percentage did Carl's Carpet Cleaning multi-factor productivity improve, in terms of dollars, from two months ago to last month? (Write your answer as a percentage, and display your answer to two decimal places.) %
Answer:
Step-by-step explanation:
Please help. Need within 40 min. Will give brainliest. 100 points! Statistics. Please give explanation too
This data does not provide sufficient evidence that the level of radon in the country is unsafe at the 0.05 level of significance.
We have taken a random sample of 32 homes and we have measured the radon level in each. The sample mean is 4.9 with a standard deviation of 2.1. Using a significance level of 5 %, we have to determine whether this data provides convincing evidence that the mean radon level in the country is too high.
State:
H1: mu = 4
H2: mu > 4 (unsafe radon level)
The parameter is an acceptably safe radon level.
The significance level (alpha) = 0.05.
We will do a one-sample t-test with a random sample, large sample size (> 30), and sample size of less than 10% of the population
t-stat = (sample mean - population mean)/(sample standard deviation/square root(sample size)
= (4.9 - 4)/(2.1/[tex]\sqrt{32}[/tex]) = 2.42
p-value = P(t > 2.42) with 31 degrees of freedom is just above 0.1 (using table value for DOF = 30).
We will not reject H1 at 0.05 level of significance as
p-value > level of significance.
Therefore, we do not have sufficient evidence that the level of radon in the country is unsafe at the 0.05 level of significance.
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A school is constructing a rectangular play area against an exterior wall of school building. It uses 120 feet of fencing material to enclose three sides of the play area. a Complete the table by giving the length and area for each build. b write an equation to represent l, the length of the play area in feet, as a function of w, the width in feet. c write an equation to represent A, the area in square feet, as a function of w, the width in feet.
An equation to represent A, the area in square feet, as a function of w, the width in feet will be; A = 120W -2W²
Here, the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
To maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have,
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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When spinning a penny, Claire believes the proportion of times the penny lands on heads is not 0.5. She spins a penny 50 times and it lands on heads 30 times. Which hypotheses would test Claire’s claim?
The hypothesis are
Null Hypothesis: The proportion of time the penny lands on heads 0.5
Alternative Hypothesis: The proportion of times the penny lands on heads in not 0.5.
We can denote the proportion of times the penny lands on heads as p.
If the null hypothesis is true, then p = 0.5. If the alternative hypothesis is true, then p is not equal to 0.5.
We can use a hypothesis test to determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. One possible hypothesis test is the two-tailed z-test for proportions.
To perform this test, we would calculate the test statistic :
z = (p' - p) / √(p x (1-p) / n)
where p' is the sample proportion, p is the null hypothesis proportion (0.5), and n is the sample size.
In this case, we have a sample size of n = 50 and a sample proportion of p' = 30/50 = 0.6. We can calculate the test statistic:
z = (0.6 - 0.5) / √(0.5 x 0.5 / 50)
z ≈ 2.24
To determine if this test statistic is significant at the 5% level, we would compare it to the critical values from the standard normal distribution. For a two-tailed test at α = 0.05, the critical values are -1.96 and 1.96.
Since 2.24 falls outside of this range, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the proportion of times the penny lands on heads is not 0.5.
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Factor the following expressions completely. Show and check all work on your own paper.
4x4+8x3+4x2
The complete factorization of the original expression is:
4x² (x + 1)²
We have,
First, we can factor out 4x².
4x² (x² + 2x + 1)
Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:
4x² (x + 1)²
Thus,
The complete factorization of the original expression is:
4x² (x + 1)²
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A fair coin is tossed 8 times. Find the probability it comes up heads at least TWICE. Will give brainliest!!
Step-by-step explanation:
At least twice means it could be 2 3 4 5 6 7 or 8 heads
there is 8 chances of having only one TAIL
there are 2^8 outcomes = 256 outcomes possible
take away the EIGHT with one tail
248 out of 256 have at least 2 heads
248/256 = 31/32
( Let me know if this is incorrect and I will re-evaluate !)
Answer:
[tex]\frac{247}{256}[/tex]
Pre-requisite Knowledge:
Permutations and Combinations
Elementary Probability
Step-by-step explanation:
Total number of outcomes (Cardinality of the sample space) = [tex]2^{8}[/tex]
P(at least 2 heads show up) = 1 - [ P(no Head) + P(exactly 1 Head) ]
[tex]= 1-\frac{C(8,0)+C(8,1)}{2^8}\\\\=1-\frac{1+8}{256}\\\\ =1-\frac{9}{256}\\\\= \frac{247}{256}[/tex]
Select the correct answer. Which logarithmic equation is equivalent to this exponential equation? 2400=7500(10)^-x
The logarithmic equation is equivalent to this exponential equation is x = log (8/25) (option c).
In this case, we are asked to find the logarithmic equation that is equivalent to the given exponential equation:
2,400 = 7,500(10)⁻ˣ
To solve for x, we need to isolate it on one side of the equation. We can start by dividing both sides by 7,500:
2,400/7,500 = (10)⁻ˣ
The choice of base for the logarithm doesn't matter, as long as we use the same base for both sides. Let's use base 10:
log(2,400/7,500) = log(10⁻ˣ)
Using the properties of logarithms, we can simplify the right-hand side:
log(2,400/7,500) = -x*log(10)
We know that log(10) = 1, so we can simplify further:
log(2,400/7,500) = -x
x = log(8/25) = log(8) - log(25) = 0.9031 - 1.3979 = -0.4948
So the only answer choice that gives us the same equation as the original exponential equation is (C) x = log (8/25).
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Complete Question:
Which logarithmic equation is equivalent to this exponential equation?
2,400 = 7,500(10)^(-x)
A. x= -log (25/8)
B. x = log(-25/8)
C. x = log (8/25)
D. x = -log (8/25)
Solve for x. Round to the nearest tenth of a degree, if necessary.
The value of angle x is 48.07 degree.
Given that,
ΔSTU is right angle triangle
TU = 7
SU = 9.4
Since sinx = opposite/hypotenuse
= TU/SU
= 7/9.4
= 0.744
⇒ sinix = 0.744
Take inverse of sinx both sides
⇒ x = 48.07 degree
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If g(x) is the inverse of f(x), what is the value of f(g(2))?
Answer:
The answer is C) 2.
Step-by-step explanation:
Since g(x) is the inverse of f(x), we know that f(g(x)) = x for all x in the domain of g.
Therefore, f(g(2)) = 2.
The answer is C) 2.
In a class of students, the following data table summarizes how many students have a
cat or a dog. What is the probability that a student chosen randomly from the class
does not have a cat?
The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
The class has a cat and a dog = 9
Has a dog and does not have a cat = 2
Does not have a dog and has a cat = 4
Does not have dog and cat = 5
The total strength of the class is 20
The probability that a student is chosen randomly from the class has a cat or a dog = Number of favorable outcomes / total number of outcomes
P(E) = 15 /20
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Answer:
Step-by-step explanation:
its 11/28
Explain why or why not the given divisions of integers will be rational
A) 0/3. B) 3/0. C) -3/8
The rational numbers are solved and the incorrect number is A = 3/0
Given data ,
Let the rational number be represented as A
Now , the value of A is
A)
The division 0/3 will be a rational number because any number divided by 0 is undefined, but in this case, the division is defined and the result is 0, which is a rational number.
B)
The division 3/0 will not be a rational number because any number divided by 0 is undefined, and therefore, the division is not defined.
C)
The division -3/8 will be a rational number because it can be expressed as a ratio of two integers (-3 and 8) and can be written in the form of a fraction -3/8
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Please help me and show work
Step-by-step explanation:
'Find the product...' just means multiply the two numbers together:
(use your calculator) 5602 x 17 = 95,234
Product means multiply them together. Please see image showing multiplication. You could also break this up into (5602 x 7) + (5602 x 10), which is basically what I did vertically.
5 1/2 feet =what to inches
Answer:
66 inches
Step-by-step explanation:
Every foot is twelve inches
Answer: 66 inch is in 5 1/2 feet
Step-by-step explanation: there is 12 inches in 1 foot so you do 12 x 5= 60 then there is 6 inches in a half of a foot so you add 60 and 6 and you get 66 inches
DATE 5 Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks), and Jose has 62 (6 bundles of 10 and 2 sticks). a Sketch Sasha's sticks in the first box and Jose's in the second box. (Hint: Use rectangle for each bundle and a line for each stick.)
There are 10 bundles and 1 sticks in the Popsicle sticks
Given that Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks)
4B+7S=47
Jose has 62 (6 bundles of 10 and 2 sticks).
6B+2S=62
We have to find B and S values
12B+21S=141
12B+4S=124
Subtract both the equations
21S-4S=141-124
17S=17
Divide both sides by 17
S=1
Now let us plug in the value of S
4B+7=47
4B=40
B=10
Hence, there are 10 bundles and 1 sticks in the Popsicle sticks
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How many schools have fewer than 50 classrooms
Answer:
7 schools have fewer than 50 classrooms.
Adrian made a cone from construction paper. the equation for the surface area of a cone is a=pi r^(2)+pi rs, where r is the radius of the base and s is slant height of the cone. dimensions of the cone are h=,8 ; r=,3
what is the total of paper needed?
The total amount of paper required is 3π(3+√71)unit²
The equation for the surface area of a cone is given as follows:
A = πr²+πrs.
Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)
Substituting the values of r & h to determine s
s = √(8²+3²)
s = √71
Substituting the values to get Area,
A=π*3²+π*3*√71.
A=3π(3+√71)
Hence, the required paper will be A=3π(3+√71)unit²
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Calculate the volume of air in cubic centimeters of a sphere with diameter = 9 centimeters. Use your calculator’s pi button and round answers to two decimal places. V=______ cm3
The volume of air of a sphere with diameter 9 centimeters is 381.51 cubic centimeters
The formula for the volume of a sphere is:
V = (4/3)πr³
where r is the radius of the sphere.
The diameter of the sphere is 9 cm, which means the radius is half of that:
r = 9/2 = 4.5 cm
Substituting this value into the formula, we get:
Volume = (4/3)π(4.5)³
Volume = (4/3)×3.14 × 91.125
Volume = 381.51 cubic centimeters
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A rectangular tank 80 cm wide by 100 cm long by 60 cm high is filled up with water up to of its height. Water is then poured into the tank until it is 3 filled with 384 € of water. Find the amount of water that was poured the tank. Give your answer in litres.
Answer:
0 liters
Step-by-step explanation:
The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:
Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³
Since the tank was filled up to of its height, the volume of water in the tank at this point is:
Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³
To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):
Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height
= 384,000 cm³ - 1,200,000 cm³
= -816,000 cm³
Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.
Therefore, the answer to the problem is 0 liters or 0 cm³.
Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.
PLEASE HELP!!!!!! I WILL MARK BRAINIEST!!!!!
g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.
Option C is the correct answer.
We have,
To find the transformation that maps f(x) to g(x), we need to determine how the points of g(x) relate to the points of f(x).
First, we can see that the two functions have the same x-coordinates (1 and 4). This means that the transformation only affects the y-coordinates of the points.
At x = 1,
f(x) has a y-value of 4, and g(x) has a y-value of 2.
This means that g(x) is f(x) after vertical compression by a factor of 1/2.
At x = 4, f(x) has a y-value of 8, and g(x) has a y-value of 4.
This means that g(x) is f(x) after vertical compression by a factor of 1/2.
Therefore,
g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.
i.e
g(x) = (1/2) f(x)
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Eight times a number
A
8+n
B
8n
C
8−n
D
8n
Answer:
The answer is D
Step-by-step explanation:
8× the number
let the number be n
8×n=8n
Answer:
8n
Step-by-step explanation:
whenever a number is attached to a variable, that means multiplication. 8n is the correct answer.
have a great day and thx for your inquiry :)
Drag one number to each box (?) to make three true statements.
1
2
3
4
5
7
6
7
8
9
3/8 x ?/? > 1
3/8 x ?/? = 1
3/8 x ?/? < 1
Answer: 638
Step-by-step explanation:1
2
3
4
5
7
6
7
8
9
3/8 x ?/? > 1
3/8 x ?/? = 1
need help will give brainlist
The expressions that shows a correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is (-4-6) / (-7 - 3) (option c).
To find the slope of a line that passes through two points, we can use the slope formula, which is:
slope = (change in y) / (change in x)
This formula tells us how much the y-coordinate changes (rise) for every one unit of change in the x-coordinate (run).
Now let's use the given points (3,6) and (-7,-4) to set up the slope formula. We'll call the first point (x₁, y₁) and the second point (x₂, y₂). Then we can plug these values into the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Plugging in the coordinates of the two given points, we get:
slope = (-4 - 6) / (-7 - 3)
We simplify this expression to get:
slope = (-10) / (-10)
Which simplifies further to:
slope = 1
So the correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is:
slope = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 6) / (-7 - 3)
= 1
Therefore, the slope of the line passing through these two points is 1.
Hence the correct option is (c).
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