A candy bar and a piece of bubble gum together cost $1.10. The candy bar costs a dollar more than the bubble gum. How much does the candy bar cost, in dollars?

Answer:

1) The null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

Subindex 1: 2012 population proportion and Subindex 2: 2010 population proportion.

2) The sample proportion for 2012 is p1=0.41.

The sample proportion for 2010 is p2=0.35.

3) There is enough evidence to support the claim that there is significant difference between the population proportions of the two years.

4) The 95% confidence interval for the difference between proportions is (0.016, 0.104).

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is significant difference between the population proportions of the two years.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=1000 has a proportion of p1=0.41.

[tex]p_1=X_1/n_1=410/1000=0.41[/tex]

The sample 2, of size n2=900 has a proportion of p2=0.35.

[tex]p_2=X_2/n_2=315/900=0.35[/tex]

The difference between proportions is (p1-p2)=0.06.

[tex]p_d=p_1-p_2=0.41-0.35=0.06[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{410+315}{1000+900}=\dfrac{725}{1900}=0.3816[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.3816*0.6184}{1000}+\dfrac{0.3816*0.6184}{900}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0003}=\sqrt{0.0005}=0.0223[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.06-0}{0.0223}=\dfrac{0.06}{0.0223}=2.69[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=2\cdot P(z>2.69)=0.007[/tex]

As the P-value (0.007) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is significant difference between the population proportions of the two years.

We want to calculate the bounds of a 95% confidence interval.

For a 95% CI, the critical value for z is z=1.96.

The margin of error, using the results previously calculated, is:

[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0223=0.0437[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.06-0.0437=0.016\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.06+0.0437=0.104[/tex]

The 95% confidence interval for the difference between proportions is (0.016, 0.104).

Answer:

13

Step-by-step explanation:

1^5 is equal to one, since 1 to any power is 1.

Then, calculate the parentheses: 8 -2 + 6 = 12.

1 · 12 = 12

12 + 1 =

13

Answer:

13

Step-by-step explanation:

1⁵=1

(8-2+6)= 12

1*(12)= 12

12+1=13

Answer:

-4 · [tex]4^{7}[/tex]

Step-by-step explanation:

Answer:

(1,0)

Step-by-step explanation:

(-1+3)/2 = 1

(-1+1)/2 = 0

what is the question? is there an image

Answer:

x < 6

Step-by-step explanation:

5x < 21 +9

5x < 30

x < 30/5

x < 6

so the value of x is 5,4,3,2,1, 0, -1, ....

Answer: x<6

Step-by-step explanation:

For this problem, we approach it as if it had an equal sign instead of an inequality.

5x-9<21      [add 9 on both sides]

5x<30         [divide 5 on both sides]

x<6

Answer:

rational

Step-by-step explanation:

it's rational because a rational number * a irrational number is always irrational. a rational number times a rational number = a rational number. here are examples:

case 1 irrational times rational:

root two * 4 = 5.65685424949

case 2  rational times rational

8 * 5 = 40

Answer:

(-3,18) and (-1,6)

Step-by-step explanation:

[tex]x^2-2x+3=-6x\\<=> x^2+4x+3 = 0\\<=> (x+2)^2 -4+3=0\\<=> (x+2)^2-1^2 = 0\\<=> (x+2+1)(x+2-1) = 0\\<=> (x+1)(x+3) = 0\\<=> x+1 = 0 \ or \ x+3 = 0\\<=> x = -1 \ or \ x=-3[/tex]

so the solutions are

(-3,-6*-3=18) that we can write (-3,18)

and

(-1,-6*-1=6) that we can write (-1,6)

Answer:

  4 hours

Step-by-step explanation:

For three visits, the electrician earned $40 × 3 = $120 in "per-visit" charges. For working x hours, he earned 20x in "per-hour" charges. The total of these came to 50x:

  120 +20x = 50x

  120 = 30x . . . . . . . . subtract 20x

  4 = x . . . . . . . . . . . . . divide by 30

The electrician worked 4 hours that day.

Answer:

-10

Step-by-step explanation:

[tex]-\dfrac{3}{5}x=6 \\\\\\x=\dfrac{6}{-\dfrac{3}{5}} \\\\\\x=6\times -\dfrac{5}{3} \\\\\\x=-10[/tex]

Hope this helps!

Answer:

x = -10

Step-by-step explanation:

So first and easily we have to multiply to --> -3/5x = 6

After that you just do the regular formula -->

Factor divided by the x

6 / (-3/5) = -10

-10

Hope this helps

Answer:

8000 cubic centimeters

Step-by-step explanation:

The surface area of a cube is 6 times the square of the side length. If we call the side length of the cube s:

[tex]6s^2=2400 \\\\s^2=400 \\\\s=20[/tex]

Since the volume of a cube is the side length cubed, the volume of this is [tex]20^3=8000\text{ cm}^3[/tex].

Hope this helps!

Answer: 70.00$

Step-by-step explanation:

The question states that it takes 20 gallons of gas to get there, and the cost of three gallons of gasoline is $10.50.

so

20/3 * 10.50=70$

Answer:

70.00$

Step-by-step explanation:

Corrected Question

A cylinder with a base diameter of x units has a volume of  [tex]\pi x^3[/tex] cubic units

Which statements about the cylinder are true? Check all that apply.

Answer:

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]

Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]

Volume =Base Area X Height

[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]

Therefore:

Answer:

Induction

Step-by-step explanation:

Induction reasoning refers to conjectures which is what you will need for this

The Inductive reasoning allows to use observation to find the next three

values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

For given example,

We have been given the number pattern 1, 4, 7, 10, . . .

Here, 4 - 1 = 3                             ..................(i)

7 - 4 = 3                                       ..................(ii)

10 - 7 = 3                                      ..................(iii)

From (i), (ii) and (iii),

the common difference between consecutive terms is 3.

The next three values would be,

10 + 3 = 13

13 + 3 = 16

16 + 3 = 19

So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .

Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

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The correct answer is B. 24

Explanation:

If you consider the shaded part of the rectangle is a triangle the best way to calculate the area of this is by calculating the total area or space occupied by this triangle. This can be done if you multiply the base by the height and divide the result in 2 or b x h / 2.

6 squares (base) x 8 squares (height) = 48 / 2 = 24 squares

Also, the shaded area is approximately the half area of all the rectangle, in this case, you can calculate the area of the rectangle by multiplying side x side or length by width. This means 6 squares x 8 squares = 48 squares (total area), which divided by 2 (shaded area) is also equal to 24.

Answer:

B, 24.

Step-by-step explanation:

I solved it with my teacher

Answer:

Option C is correct.

The 437 county residents were a random sample of all county residents.

a) If p is the proportion of Hispanics in the county,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.35

b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.

c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

Test statistic = -4.09

p-value = 0.000043

d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.

Step-by-step explanation:

According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.

a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).

Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).

The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).

Mathematically,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.16

b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.

Hence, the model of this test is two-tailled, one-proportion test.

And the major conditions for an hypothesis test is that

- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.

- The sample must be a normal distribution sample or approximate a normal distribution.

The conditions to check this is that

np ≥ 10

and

np(1-p) ≥ 10

p = sample proportion = (44/437) = 0.101

np = 437×0.101 = 44 ≥ 10

np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10

The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.

c) So, we compute the t-test statistic

z = (x - μ)/σₓ

x = sample proportion = 0.101

μ = p₀ = The proportion we are comparing against = 0.16

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 437

σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144

z = (0.101 - 0.16) ÷ 0.0144

z = -4.093 = -4.09

checking the tables for the p-value of this z-statistic

Degree of freedom = df = n - 1 = 437 - 1 = 436

Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)

The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).

p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043

The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

d) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.000043

0.000043 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.

Hope this Helps!!!

Answer:

9/25

Step-by-step explanation:

15 red marbles, 7 yellow marbles, and 3 pink marble = 25 marbles

1st marble red

P(red) = red/total = 15/25 = 3/5

replace

15 red marbles, 7 yellow marbles, and 3 pink marble = 25 marbles

2nd marble red

P(red) = red/total = 15/25 = 3/5

P(red, replace,red) = P(red) * P(red) = 3/5 * 3/5 = 9/25

Answer:

The volume of the container is 1584 inch³.

Step-by-step explanation:

The volume of a rectangular prism is:

[tex]\text{Volume}=\text{l}\times\text{w}\times\tect{h}[/tex]

It is provided that the container is made up of two rectangular prisms.

The dimensions are as follows:

Compute the volume of the rectangular prism 1 as follows:

[tex]\text{V_{1}}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}[/tex][tex]\text{V}_{1}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}[/tex]

    [tex]=14\times 6\times 16\\=1344[/tex]

Compute the volume of the rectangular prism 2 as follows:

[tex]\text{V_{1}}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}[/tex][tex]\text{V}_{2}=\text{l}_{2}\times\text{w}_{2}\times\text{h}_{2}[/tex]

    [tex]=10\times 6\times 4\\=240[/tex]

Then the volume of the container will be:

[tex]\text{Volume of container}=\text{V}_{1}+\text{V}_{2}[/tex]

                             [tex]=1344+240\\=1584[/tex]

Thus, the volume of the container is 1584 inch³.

Answer:

Step-by-step explanation:

What is the volume of the container below?

2 rectangular prisms. A rectangular prism has a length of 14 inches, width of 6 inches, and height of 16 inches. A rectangular prism has a length of 10 inches, width of 6 inches, and height of 4 inches.

576 inches cubed

1,080 inches cubed

1,584 inches cubed

1,920 inches cubed

Answer:

Heun's method is also known by its other name called Modified Euler methods. This method is used in computational or mathematical science.

Step-by-step explanation:

Euler method is the method that is also pronounced in two similar stages such as Runge- Kutta methods. This method has been named after Dr. Heun.

This method is used for the solution of ordinary differential equations with its given values. There is some method to calculate this method. The improved Runge Kutta methods are also called the Butcher tableau method, the other methods are also called the Ralston methods.

Step-by-step explanation:

I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.

Really all you need to do is use PEMDAS for the first question.

(Parentheses, exponents, multiply, divide, add, subtract. In that order)

[tex]1 2 + 8 \div (9 - 5) \\ 12 + 8 \div 4 \\ 12 + 2 \\ 14[/tex]

Then to simplify that fraction next to it, notice that 0.018 is 3x 0.06.

that's a 3:1 ratio, so it ends up simplifying to this:

[tex] \frac{3}{1} [/tex]

Lastly, to solve the division of that fraction. If you divide by a fraction, you multiply whatever it's dividing by its inverse.

So...

[tex] \frac{5}{7} \div \frac{2}{5} \\ \frac{5}{7} \times \frac{5}{2} \\ \frac{25}{14} [/tex]

The curved arcs indicate which angles are congruent with one another. The single arcs on angles R and I mean these two angles are congruent. The double arcs on angles Q and H are the other pair of congruent angles.

So far we have taken care of the two "A"s in "AAS". What we're missing is the "S", which refers to the side. This side cannot be between the two angles, otherwise we'd be talking about ASA instead of AAS.

There are two possible answers here

if either one of those congruences are true, then we have enough to use AAS

Some books use SAA in place of AAS, and they're the same thing.

Answer:

4 C, 5 C

Step-by-step explanation:

4) Sum of all candies = 14

Total number of cherry candies = 5

probability of not getting a cherry candy = 14-5 / 14 = 9/14

5) Number of supporters for Lyshon = 14

Total number of supporters = 100

Probability that a student chosen at random will vote vote for lyshon =

14/100 = 7/50

Answer:

  37

Step-by-step explanation:

I find 37 numbers in that range:

  {0, 1/16, 1/8, 1/5, 1/3, 1/2, 3/4, 4/5, 1, 5/4, 4/3, 2, 3, 7/2, 15/4, 4, 17/4, 9/2, 5, 6, 7, 8, 9, 12, 15, 16, 17, 20, 24, 28, 32, 36, 48, 60, 64, 68, 80}

For these numbers we have used only the indicated operations. No minus signs were used.

_____

Additional comment

Of the 320 ways the numbers can be combined, 15 result in division by zero. Many other results are outside the 0-99 range of interest. In total, there are 56 unique rational results.

Answer:

We know that x = 10. But, we don't know what f is. In order to find f, we would divide. To divide we would use this formula: 8 ÷ 10. This equals 0.8 or 8 tenths. Now, we know what our f value is. It's 0.8! To double check, use a calculator and type in: 10*0.8 and see if the answer is 8. (Please mark brainliest! :D)

Answer:

Step-by-step explanation:

The exact value of tan 4π/3 is √3.

Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

We have to find the exact value of tan4pi/3.

tan 4π/3

= tan (π + π/3)

= tan (π/3)

= √3.

So, the value is √3.

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Answer:

see below

Step-by-step explanation:

6 cot ^2 (y) ( sec^2 (y) -1) = 6

We know that ( sec^2 (y) -1) = tan ^2(y)

6 cot ^2 (y) tan ^2 (y) = 6

We know cot = cos/ sin   and tan = sin / cos

6 cos/ sin ^2 (y) sin/cos ^2 (y) = 6

6 ( 1) = 6

6=6

Answer:

See below

Step-by-step explanation:

[tex]6\cot^2(\gamma)(\sec^2(\gamma)-1)=6\\\\\\\\cot^2(\gamma)(\sec^2(\gamma)-1)=1\\\\\\\dfrac{\cos^2(\gamma)}{\sin^2(\gamma)}\left(\dfrac{1}{\cos^2(\gamma)}-1\right)=1\\\\\\\dfrac{1}{\sin^2(\gamma)}-\dfrac{\cos^2(\gamma)}{\sin^2(\gamma)}=1 \\\\\\\csc (\gamma) - \cot (\gamma)=1 \\\\\\1=1 \\\\QED[/tex]

Hope this helps!

Step-by-step explanation:

81 + 9 - 9

= 81

81 tan(45)

= 81

Answer: 81

Step-by-step explanation:

tan(45)=1

9*9+9-9

=81-0

=81tan45

=81

Answer:

[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]

Step-by-step explanation:

[tex]6(1)-2=4[/tex]

[tex]6(2)-2=10[/tex]

[tex]5 \times 3^{(3)-1}=45[/tex]

[tex]5 \times 3^{(4)-1}=135[/tex]

[tex]5(-1^{(5)}+3)=10[/tex]

[tex]5(-1^{(6)}+3)=20[/tex]

a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)

b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹

c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is  an = 10 + 10 * ((n + 1) % 2)

(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.

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Answer:

[tex]g(x)=\frac{1}{8} x^{2}[/tex]

Step-by-step explanation:

Expansions and compressions are transformations that change the length or width of the graph of a function. The general form of the graph of a function expands or compresses vertically or horizontally. Expansions and compressions are considered non-rigid transformations.

Vertical compression:

[tex]y=kf(x)[/tex]

So, if [tex]f(x)=x^{2}[/tex]  is vertically compressed by a factor of 8. Hence, using the previous information, we can conclude that the equation of [tex]g(x)[/tex] is:

[tex]g(x)=\frac{1}{8} x^{2}[/tex]

I attached you the graphs.