20.
Building on the Essential Question How can
you check to see if two fractions are equivalent? Explain.
?
08 Chapter 8 Fractions

Answer:

The answer is C and D

Explanation:

The angle of an equilateral triangle will always be 60 degrees and all the sides will be equal so that leaves us with D. A triangle can't have any parallel sides or it won't be a triangle

Answer:

a. true

b. true

c. false

d. false

We have the following:

The standard deviation of the number of defective candles in a group of 45 candles selected off the production line would be 1.67.

This can be calculated using the formula for the standard deviation of a binomial distribution:

sqrt(np(1-p))

where:

n = 45 (the sample size)

p = 0.037 (the probability of a defective candle)

Plugging in the values:

sqrt(45 * 0.037 * (1 - 0.037)) = sqrt(45 * 0.037 * 0.963) = sqrt(1.67) = 1.67

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There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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Answer:

C- Chi-square test for Homogeneity

Step-by-step explanation:

Because you're looking for whether there are regional differences in peanut butter into 7 different samples, that means you're searching for i categorical variable in the 7 different random samples, making it a chi-square for homogeneity.

The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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Answer:

The three consecutive integers are 19, 20, and 21. And 19 + 21 = 40.

Step-by-step explanation:

Let the first integer be x.

The next consecutive integer would be x + 1 and the next x + 2.

The equation for the sum of the first and third integer equaling 40 can then be written as:

x + (x + 2) = 40

Solving gives:

2x + 2 = 40

2x + 2 - 2 = 40 - 2

2x = 38

x = 19

Based on Lauren's spending patterns and the balance in her account, her new balance must be an overdraft of $180.

Her balance after the vacation can be found as:

= Balance before vacation - ( Amount spent)

= 60 - ( 80 x 3)

= 60 - 240

= -$180

In conclusion, she will have a bank overdraft of $180.

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Answer:

Option (2) and Option (4)

Step-by-step explanation:

From the picture attached,

Length of ladder AC = 20 feet

Height of the highest point of the ladder from ground AB = 16 ft

By Pythagoras theorem,

AC² = BC² + AB²

BC² = AC² - AB²

BC = \(\sqrt{(20)^2-(16)^2}\)

     = \(\sqrt{400-256}\)

     = \(\sqrt{144}\)

     = 12

Now, Sinθ = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}\)

                 = \(\frac{16}{20}\)

Cosθ = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}\)

         = \(\frac{12}{20}\)

tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{\text{AB}}{\text{BC}}\)

        = \(\frac{16}{12}\)

Therefore, Option (2) and Option (4) are the correct options.

The equation that should be used is option 2 and option 4.

Since

Length of ladder AC = 20 feet

Height of the highest point of the ladder from ground AB = 16 ft

So here we apply the Pythagoras theorem,

AC² = BC² + AB²

BC² = AC² - AB²

So,

\(BC = \sqrt{(20)^2 - (16)^22}\\\\ = \sqrt{400 - 256}\\\\ = \sqrt{144}\)

= 12

Now

Sin θ = 16\20

Cos θ = 12\20

tan θ = 16 \12

hence, The equation that should be used is option 2 and option 4.

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The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Answer: 6.

Step-by-step explanation: To find the mean, the first step is to add all the data together.  Here's how it should look:

2 + 3 + 6 + 6 + 7 + 8 + 8 + 8 = 48.

Next, you need to divide whatever you get after adding the data by how many numbers there are for your data.  In this case, 48 was the answer when we added all the data.  In total, you have 8 numbers in your data, so you need to divide 8 from 48.  It should look like this:

48 / 8 = 6.

Therefore, the mean for this data set is 6.

Have a great day! :)

Answer:

$20 + (1.75 * p)

Step-by-step explanation:

This is just a guess hope this is correct.

Hope this helps! :)

Answer:

0.5 or 1/2

Step-by-step explanation:

-1+3[(10-12)^3÷(-16)]

(10-12)^3÷(-16)

(-2)^3=-8

-8÷(-16)=0.5

Answer:

(0,-3) (2,0) (-2,-6) (0.66,-2)

Step-by-step explanation:

Please see the attached graph for the plotted points.

I hope this helps.

Answer:

-10

Step-by-step explanation:

If the axis of symmetry is at x = -3 and one of the zeros is at 4 then the other zero must be at equal distance from the axis , but on the other side, so will be at -10.

Answer:

–10

Step-by-step explanation:

got it right

The day in which Chloe would have more money than Kenzi is after 15 days.

The equation that represents the amount left after the purchase of Frutti Tutti and lunch is:

Amount left = amount she began with - (amount spent x number of days)

Amount that Chloe has left : $75 - $3x

Amount that Kenzi has left : $90 - $4x

The inequality that can be used to represent when Kenzi would have less money than Chloe is:

$75 - $3x > $90 - $4x

$4x - 3x > $90 - $75

x > 15

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Answer:

102.96

Step-by-step explanation:

Answer:

\(102.96\)

Step-by-step explanation:

7 . 2

× 14 . 3

___________

²2 . 16

²28 . 80

72 . 00

____________

¹1¹02.96

Therefor, the answer is 102.96

Answer:

\(V =\frac{12}{5}\ cm^3\)

Step-by-step explanation:

The Volume of Rectangular Prism

Given a rectangular prism of dimensions W, L, and H, its volume is the product of the three dimensions:

V = WLH

The figure shows the dimensions:

L=3 cm

\(W=\frac{4}{3}\ cm\)

\(H=\frac{3}{5}\ cm\)

Thus, the volume is:

\(V =3*\frac{4}{3}*\frac{3}{5}\ cm^3\)

\(V =\frac{36}{15}\ cm^3\)

Simplifying:

\(\boxed{V =\frac{12}{5}\ cm^3}\)

Answer:

There are 55 rooms

Step-by-step explanation:

There are 165 beds in the hospital. Each room contains 3 beds. In order to find the number of beds per room, take the total number of beds and divide it by the number of rooms in each bed. 165/3=55. There are 55 rooms in the hospital, all containing 3 beds.

Hope this helps!

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

------------------

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer:

90  berries

Step-by-step explanation:

Answer:

triangle, circle

Step-by-step explanation:

I put a link at the bottom to show you how i got my answer

The vertical cross-section of a cone is a triangle. The horizontal cross-section is a circle

Answer:

48

Step-by-step explanation:

you add 12 to y side and 2 to the x side

Answer:

48

Step-by-step explanation:

12x1=12 12x2=24 12x3=36 12x4=48

Answer:

\(Amount = \frac{10}{3}L\)

Step-by-step explanation:

Given

\(Water = \frac{4}{3}L\)

\(Plants = \frac{2}{5}\)

Required

Amount of water for the whole plants

The amount of water for the whole plants is calculated as:

\(Amount = \frac{Water}{Plants}\)

This gives:

\(Amount = \frac{4}{3}L/\frac{2}{5}\) --- The division equation

Convert division to multiplication

\(Amount = \frac{4}{3}L*\frac{5}{2}\) --- The multiplication equation

Solving further:

\(Amount = \frac{4*5}{3*2}L\)

\(Amount = \frac{20}{6}L\)

Simplify:

\(Amount = \frac{10}{3}L\)

Answer:

Step-by-step explanation:

Answer:181,250

Step-by-step explanation:

Basically, the cost would go up 5 percent, and you’re asking how much it would go up in 5 years. So 5x5=25, so you’d multiply 145,000 by 25%, which is 36,250. So, you’d add that to 145,000 which would get you 181,250.

Answer:

X is the variable and x means multiplication symbol.

X + (X x 3 - 1) + (X x 3 - 1) - 4) ≥ 45 is the answer I got.

The answer to that inequality would be

X ≥ 7

Step-by-step explanation:

I am not good at math I just tried my best sorr if it is wrong.

Answer:

Diamonds: 20 Emeralds: 1 Rubies: 24

Step-by-step explanation:

45 = Total

Diamonds = 20 (4 less than rubies)

Emeralds = 1 (made into the smallest number)

Rubies = 24 (4 more than diamonds)

Tip! To help find the answer I divided 45 into three groups so the diamonds, emeralds, and rubies all started with 15. I then started to work it into place where diamonds were ALWAYS 4 less than rubies and just kept taking away from emeralds.

<3 Enjoy,

    Dea

Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

Dish D has the density of clusters closest to 0.75 per square centimeter.

A substance's density is determined by how much mass there is per unit volume. It is typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

To find the density of clusters in each circular dish, we need to calculate the area of each dish and divide the number of clusters by that area.

The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, we are given the diameter of each circular dish, which is 8 cm. Therefore, the radius of each dish is 4 cm.

The area of each dish is:

A = πr² = π(4 cm)² ≈ 50.27 cm²

Now, we can calculate the density of clusters in each dish:

Density in A = 53 clusters / 50.27 cm² ≈ 1.05 clusters/cm²

Density in B = 13 clusters / 50.27 cm² ≈ 0.26 clusters/cm²

Density in C = 151 clusters / 50.27 cm² ≈ 3.00 clusters/cm²

Density in D = 38 clusters / 50.27 cm² ≈ 0.76 clusters/cm²

Therefore, dish D has the density of clusters closest to 0.75 per square centimeter.

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The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

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