Multiple choices answer and explain the solution?

Answer:

The discriminant of the equation is less than zero. The gymnast's hands do not reach a height of 11 feet

Step-by-step explanation:

The gymnast's hands does not reach a height of 11 feet above the trampoline.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is a[tex]x^{2}[/tex] + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

It is given that ,

h= [tex]-16x^{2} +12x[/tex]

11-6= [tex]-16x^{2} +12x[/tex]

5 = [tex]-16x^{2} +12x[/tex]

[tex]-16x^{2} +12x[/tex] -5=0

Comparing the above equation with the standard form of quadratic equation [tex]ax^{2} +bx+c=0\\[/tex]

we get ; a=-16, b=12, c=-5

Using Discriminant method

D= [tex]\sqrt[]{b^{2} - 4*a*c}[/tex]

  = [tex]\sqrt[]{(12)^{2} - 4* (-16)*(-5)}[/tex]

  = [tex]\sqrt[]{144-320}[/tex]

  = [tex]\sqrt[]{-176}[/tex]

Hence D<0, which means there is no real value.

So, the gymnast's hands does not reach a height of 11 feet above the trampoline.

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Answer:

A is correct.

Step-by-step explanation:

Left figure's area = base x height = L x h x 6 = 6Lh

Right figure's area = L x h + L x h + L x h + L x h + L x h + L x h = 6Lh

Hope this helps!

:)

Answer:

Step-by-step explanation:

Given that:

A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.

a)

Thus; we formulate the null and the alternative hypotheses as follows:

The proportion is ; [tex]\frac{64}{100}[/tex] = 0.64

Null hypothesis:    [tex]{H_0}:p = 0.64[/tex]  

The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

Alternative hypothesis: [tex]{H_a}:p \ne 0.64H[/tex]

The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

b)

The proportion of the population = 0.64

The sample size n = 100

The number of shoppers = 52  stating that the supermarket brand was as good as the national brand

The sample proportion [tex]\hat p = \frac{52}{100}[/tex]

[tex]\hat p = 0.52[/tex]

The z - value is calculated by the formula:

[tex]z = \dfrac{\hat p-p}{\frac{\sqrt{ p(1-p)}}{100 }}[/tex]

[tex]z = \dfrac{0.52-0.64}{\frac{\sqrt{ 0.64(1-0.64)}}{100 }}[/tex]

[tex]z = \dfrac{-0.12}{0.048 }}[/tex]

z = -2.50

Since z = -2.50

the p-value = 2P(Z ≤ -2.50)

p-value = 2 × 0.0062

The p-value = 0.0124

c)

At  significance level,  ∝ = 0.05 ; The p-value = 0.0124

According to  the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05

Hence, the p-value =0.0124 < ∝ (=0.05)

According to the reject rule; reject null hypothesis.

Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.

d) we know that the significance level of ∝  = 0.05

The value[tex]{z__{0.05}}[/tex]  is obtained as:

[tex]P\left( {\left| Z \right| \le z} \right) = 0.05[/tex]

Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the  first column is reached and  the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area  to the left of z

This implies that :[tex]P(Z \leq -1.96)=0.05[/tex]

The critical value for left tail is -1.96 and the critical value for right tail is 1.96.

Conclusion:

The critical value is -1.96 and the value of test statistic is - 2.50.  Here, we can see that  the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.

Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.

Following are the solution to the given points:

For point a:

Calculation of the hypotheses:

Null hypothesis [tex]\ H_0:p=0.64 \\\\[/tex]

Alternative hypothesis [tex]\ H_a : p \neq 0.64[/tex]

For point b:

 Checking the value:  

[tex]\to np_0=100 \cdot 0.64=64>5\\\\\to n(1-p_0)=100\cdot(1-0.64)=100 \cdot 0.36= 36 > 5[/tex]

Test statistic:

[tex]\to Z= \frac{0.52-0.64}{\sqrt{\frac{0.64 \times 0.36}{100} }}=-2.50[/tex]

Since there are two-sided for the test. so, [tex]z=-2.50[/tex] is negative.

Calculation of the P-value:  [tex]\to p=2P(z \leq -2.50)=2 \cdot 0.00621=0.01242<\alpha =0.05[/tex]

For point C:

In this choice, the Null hypothesis value should be rejected.

For point D:

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Answer:

3

Step-by-step explanation:

you have to multiply by 9.

2times9=18,5times 9=45,4times 9=36,

3times9=27.

Answer:

I think you are correct. bc you have 4 different caps, and four different sections of a spinner that are equal same with the cap. So I believe so.

Step-by-step explanation:

I hope this helps! Im in algebra 2 so its been awhile since i have done this. Good Luck!!:)

Answer:

A

Step-by-step explanation:

I agree with your answer. The question is basically just saying the beverage company randomly chooses one of those letters to put under the bottle caps. For example, one bottle cap might have a T on it, and another might have an A on it. If you try to get all 4 letters, then you will have to keep buying those drinks until you manage to collect all 4 letters. Therefore, there are only 4 possible options for which letter you can get.

If you spin a spinner that has 4 equal sections, then this is similar. You have 4 possible options you can get.

Hope this helps! :)

Answer:

-19

Step-by-step explanation:

12x - 6 + 6 = 10x - 40 + 2

12x - 10x = -40 + 2 + 6 -6

2x = -38

x = -38/2 = -19

The two truths are:

x is a negative number (x = -19)

x+5>x (if x is positive, is true; if x is negative, is also true)

The one lie is:

3x > 2x (if x is negative, the expression will be 3x < 2x)

The original translation < 3, -3 > moves the figure 3 units to the right and 3 units down.

We undo this by moving 3 units left and 3 units up, which is what < -3, 3 > describes.

The translation <-3, 3> will move the image back to the preimage original position.

The displacement of a image from one place to another is called translation of image.

If a figure is on the origin, i.e. (0, 0), then if turns 3 cells right.

We can see that, It translated as (3,0)

Again if it go down 3 cells, then the translated one is (3, -3)

So, moving it back, we should translate it 3 cells left & 3 cells up.

So after translation, it should be (-3, 3).

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Answer:

1:3

Step-by-step explanation:

:))

1:3

15 / 15 = 1

45 / 15 = 3

So its 1:3

Answer:

7/20

Step-by-step explanation:

35/100 is simplified to 7/20. Here is another example with a different percentage. Change 25% to a fraction. 25/100 is simplified to 1/4

Answer:

8 = -1 (x - 2)

:)

Answer:

8 = -1 (x - 2)

Step-by-step explanation:

Answer:

[tex]\large \boxed{\text{12.8 m}^{2}}[/tex]

Step-by-st ep explanation:

Assume the room is like the image below.

The formula for the area of a trapezoid is  

A = ½(a + b)h,

where a and b are the lengths of the parallel sides and h is the distance between them.

Data:

a = 3.8 m

b = 2.6 m

h = 4    m

Calculation:

[tex]\begin{array}{rcl}A & = & \dfrac{1}{2}(a + b)h\\\\& = & \dfrac{1}{2}(3.8 + 2.6)\times 4\\\\& = & \dfrac{1}{2}(6.4) \times 4\\\\A & = & \dfrac{1}{2}\times25.6\\\\& = & \textbf{12.8 m}^{\mathbf{2}}\\\end{array}\\\text{The area of the room is $\large \boxed{\textbf{12.8 m}^{\mathbf{2}}}$}[/tex]

Answer:

did it

Step-by-step explanation:

Answer:

Diameter = 22.9 ft

Step-by-step explanation:

We are told that volume of the sphere is 6329 ft³

Now formula for volume of sphere is given as;

V = (4/3)πr³

Thus,

(4/3)πr³ = 6329

Multiply both sides by 3/4 to get;

πr³ = (6329) * 3/4

πr³ = 4746.75

Divide both sides by π to obtain;

r³ = 4746.75/π

r = ∛(4746.75/π)

r = 11.4749 ft

Now, diameter = 2 x radius

Diameter = 2 × 11.4749

Diameter = 22.9498 ft

Approximating to a tenth of a feet gives;

Diameter = 22.9 ft

Answer:

Sin theta = -1/2

Step-by-step explanation:

pi < =theta <= (3pi)/2.

The above expression shows we are dealing with angle on the 3rd quadrant.

I.e greater than 180 but less than 270.

So sin tita = (√3)/2

But sin and cos are all negative in the third quadrant.

So tita = sin^-1(√3)/2

tita = 60°

Cos tita = cos 60

Cos tita = cos 60

Cos60 = 0.5

Cos 60 = 1/2

If

sin theta = -(sqrt(3))/2

Sin theta = -1/2

Answer:

cos^-1(.17) is 1.40 in radian

Step-by-step explanation:

Given cos^-1(.17), the equivalent is 80.212

This is approximately 80.21°

Which is 1.40 in radian

Answer:

a) The mean is 0.15 and the standard error is 0.056.

b)  1. Yes

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportions p, in samples of size n, the mean is [tex]\mu = p[/tex] and the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]. The Central Limit Theorem applies is np > 5 and np(1-p)>5.

In this question:

[tex]n = 40, p = 0.15[/tex]

So

(a) Find the mean and the standard error of the distribution of sample proportions.

[tex]\mu = 0.15, s = \sqrt{\frac{0.15*0.85}{40}} = 0.056[/tex]

So the mean is 0.15 and the standard error is 0.056.

(b) Is the sample size large enough for the Central Limit Theorem to apply?

np = 40*0.15 = 6 > 5

np(1-p) = 40*0.15*0.85 = 5.1>5

So yes

The standard error of the distribution of sample proportions is 0.056 and mean is 0.15.

Yes, the sample size is enough for the Central Limit Theorem to apply.

(a). Given that, size of sample, [tex]n=40[/tex]

        Proportion, [tex]p=0.15[/tex]

In the distribution of sample proportions, mean [tex]\mu=p[/tex]  

and, standard error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

So, mean [tex]\mu=0.15[/tex]

Standard error =[tex]\sqrt{\frac{0.15(1-0.15)}{40} }=0.056[/tex]

(b). The Central Limit Theorem applies if np > 5 .

 [tex]np=40*0.15=6>5[/tex]

Thus, the Central Limit Theorem is applied.

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Answer:

[tex]\sqrt[4]{10x2}[/tex]

Answer:

⁴√10√x

Step-by-step explanation:

⁴√5x*⁴√2x

⁴√5x = ⁴√5⁴√x

=⁴√5 ⁴√x⁴√2x

⁴√2x = ⁴√2⁴√x

=⁴√5⁴√2⁴√x⁴√x

⁴√x⁴√x = x1/4x1/4 = x1/4+1/4

=⁴√5⁴√2⁴x1/4+1/4

1/4+1/4 = 1/2

=⁴√5⁴√2⁴√x

⁴√5⁴√2⁴ = ⁴√5*2

=⁴√5*2√x

5*2 = 10

= ⁴√10√x

Answer:

$275

Step-by-step explanation:

Day                                   Price                     Unit price

Monday                            $245                        $2.45

Tuesday                           $315                          $3.15

Wednesday                     $275                         $2.75

Thursday                         $200                         $2.00

Friday                              $225                         $2.25

the first in, first out (FIFO) method uses the price of the oldest units to determine the cost of goods sold:

the ending inventory should = 100 units purchased Friday + 25 units purchased Thursday = (100 x $2.25) + ($25 x $2) = $225 + $50 = $275

Answer: $375

Step-by-step explanation:

Answer:

11x+5/x

Step-by-step explanation:

Answer:

A.

The electrons move back and forth.

Step-by-step explanation:

i took the test

Answer: 24

Step-by-step explanation:

7+12+5=24

Answer:

24

Step-by-step explanation:

Answer: 4,588.4 cubic centimeters.

Step-by-step explanation: 20 centimeters ⋅ 14 centimeters = 280 centimeters = 4588.38 cubic centimeters = 4,588.4 cubic centimeters.

Answer:

a) (-1,0) and (3,0)

b) x=1

c) (1, -4)

Step-by-step explanation:

As you can see in the graph below, the x intercepts of this graph are at (-1,0) and (3,0), the axis of symmetry is x=1, and the vertex is at (1,-4). Hope this helps!

Answer:

okay

Step-by-step explanation:

2^3 times 3^2

Answer:

2^3*9

Step-by-step explanation:

72-9

8-2

4-2

2-2

1

Answer:

g(x) = 4x - 1

Step-by-step explanation:

Linear function in the format: g(x) = ax + b

g(2t) is a*(2t)+b

g(2t) = 8t - 1 means that:

when x = 2t, g = 8t - 1.

So

Equaling both sides

8t - 1 = a*2t + b

So

b = -1,

and

2a = 8, a = 8/2, a = 4

So

g(x) = 4x - 1

Greatest number of bricks Lynn can make is 10 and 4 pounds of the mixture will be washed out of the bucket

Pounds of water = 39

Pounds of brick dust = 48

Total mixture = 87 pounds

Mixture spilled = 13 pounds

Mixture remaining = 87 pounds - 13 pounds

= 74 pounds

Mixture in each brick holes = 7 pounds of mixture

Greatest number of bricks Lynn can make = Mixture remaining ÷ Mixture in each brick holes

= 74 pounds ÷ 7 pounds

= 10 remaining 4 pounds

Therefore,

Greatest number of bricks Lynn can make is 10 and 4 pounds of the mixture will be washed out of the bucket

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Answer: Greatest number lynn can make is 10 Bricks.

4 pounds will be washed out the bucket.

Step-by-step explanation:

Answer:

1- Inverses .

2 - Not inverses.  

Step-by-step explanation:

Notice that

1 -

[tex]f(g(x))= 3/(3/x) = (3x)/3 = x[/tex]

Since their composition is the identity, then they are inverses.

2 -

[tex]f(g(x)) = ((-x+4)+4) = -x+8[/tex]

Since their composition is not the identity, then they are not inverses.