I need to know the unit price for both a and b and what’s the better buy

Answer:

8 and 6

Step-by-step explanation:

If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.

You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.

The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.

Next, we add 10 to both sides. This gives 8x=64.

From there, we isolate the x by dividing both sides by 8, giving x=8.

To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).

This comes to y=8-2, therefore y=6.

**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!

Answer: The answer I came up with is:  $237,737

The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:

\(dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.\)

By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.

The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))\((4e^t)\).

To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.

The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).

Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).

Similarly, differentiating\(y = 4e^t\) with respect to t yields \(dy/dt = 4e^t.\)

Now we can apply the chain rule:

dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt

Substituting the expressions for x, y, dx/dt, and dy/dt:

\(dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)\)

Simplifying this expression will yield the final result.

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Answer:

\( \frac{3393939}{10000000} \)

Step-by-step explanation:

\(0.(3)3(9) = \frac{3393939}{10000000} \)

The simple regression line is used to estimate the population regression line.

We are asked about, the simple regression line

We have options:

a. is estimated by the population regression line.

b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.

c. shows the actual (or true) relation between the dependent and independent variables.

d. is used to estimate the population regression line.

e. connects the data points in a sample.

From the above options, Option (d) is the correct one i.e. is used to estimate the population regression line.

The simple regression line is used to estimate the population regression line.

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Answer:

Step-by-step explanation:

(x+7)/2= -8

x + 7 = -16

x= -23

(y + 1)/2 = -9

y + 1 = -18

y = -19

(-23, -19)

Answer:

Brainliest please

Step-by-step explanation:

perimeter is to add all sides

73m= 16+B+C

{ use algebra}

C is a, B is twice C, hence 2a

a+2a(+16)=73

3a=73-16= 57

3a=57, divide

a= 19

B=19×2= 38m

C=19m

C is 19m

Answer:

C = 19 m

Step-by-step explanation:

Side B is twice the length of Side C.

B = 2C -----------(I)

Perimeter = 73 m

A + B + C = 73

A + 2C + C = 73  {from (I)}

16 + 3C = 73

3C = 73 - 16

3C = 57

C = 57/3

C = 19 m

Answer:

He would be about 69 inches

Answer:

69 inches tall

Step-by-step explanation:

add 5ft = 60 inches + the other 9 inches which is

69 inches all together

The required sample size is 611 students to estimate the fraction of tenth graders reading at or below the eighth grade level with a 85% confidence level and an error of at most 0.03.

To calculate the required sample size, we need to consider the formula for sample size in estimating population proportions. The formula is given by:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n = sample size

Z = z-score corresponding to the desired confidence level (in this case, 85% corresponds to a z-score of approximately 1.44)

p = estimated population proportion

E = maximum error

Plugging in the given values, we have:

n= (1.44^2 * 0.15 * (1 - 0.15)) / 0.03^2

The required sample size is 611 students to estimate the fraction of tenth graders reading at or below the eighth grade level with a 85% confidence level and an error of at most 0.03.

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Answer:

a. (5, 10).

Step-by-step explanation:

When the equation is (x - 5)^2 + (y - 10)^2, you can find the center from that. The x-coordinate of the center will be x - 5 = 0, so x = 5. The y-coordinate for the center will be y - 10 = 0, so y = 10.

Your center of the circle will be a. (5, 10).

Also, if you want to know the radius, you find the number to the right of the equation (in this case, (10)^2), and find the square root of the number. So, the radius of this circle is 10 units.

Hope this helps!

Answer:

Step-by-step explanation:

Hence, Option A (-26x² + 56x - 15) is correct.

Hoped this helped.

\(BrainiacUser1357\)

The equivalent expression to the one given is x⁶y⁴/xy²

Given the expression :

opening the bracket :

The Numerator:

(x²y)(x⁴y³) = x⁶y⁴

The denominator:

xy² = xy²

Hence, we have:

(x²y)(x⁴y³)/xy² = x⁶y⁴/xy²

Therefore, the equivalent expression is x⁶y⁴/xy²

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Answer:

How many standard deviations above the mean is 14,500 hours? 1.25 1.5 2.5 Using the standard normal table, the probability that Seth's light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is about ✔ 89% .

Answer:

89%

Step-by-step explanation:

brainliest please

Answer:

2198.9 cm³

Step-by-step explanation:

Volume of flower vase = volume of cuboid - voume of cone

Volume of cuboid = lbh (length×breath×height) = 12 × 10 × 20 = 2400 cm³

Volume of cone = ⅓ × base area × height

Base area = area of circle = pi radius² = pi 4² = 16 pi

(the diameter of the circle is 8 so to find the radius you just divide it by 2 and you'll get 4)

So,

vol of cone = ⅓ × 16 pi × 12 = 64 pi = 201.06192

Volume of flower vase = 2400 - 201.06192 = 2198.93808 = 2198.9

The sample size which is required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03 is equals to the 382.

We have provide that the state education commission wants to draw an estimate on the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Population proportion, p = 0.21

confidence level = 85%

Margin of error = 0.03,

We have to determine the sample size. For determining sample size for estimating a population propotion, using the below formula,

n = (Zα/2)² ×p×(1-p) / MOE²

where MOE is the margin of error

Using the distribution table, Zc for 85% for confidence level where α = 0.15 or α/2 = 0.075 equals to the 1.439.

Substituting all known values in formula we

n = 1.439² × 0.21( 0.79)/ (0.03)²

=> n = 382.2336 ~ 382

Hence, required sample size is 382.

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Ans a) Using a standard normal distribution table or calculator, the p-value for a two-tailed test with a test statistic of 1.4142 is 0.1576 (rounded to four decimal places).

Ans b) Using a standard normal distribution table or calculator, the p-value for a two-tailed test with a test statistic of 4.4843 is less than 0.0001 (rounded to four decimal places).

Ans c) Yes, the small p-value for n = 500 indicates a significant difference between the true average fracture toughness values of the two types of steel.

Ans d)  No, a report of the p-value alone would not be sufficient.

The following is a solution to the problem. To decide whether two different types of steel have the same true average fracture toughness values, n specimens of each type are tested, yielding the following results. The sample average for type 1 is 60.9, and the sample SD is 1.0. For type 2, the sample average is 60.7, and the sample SD is 1.0. We assume that the data is based on n = 100 and n = 500.

Solution a) We will now calculate the p-value for the appropriate two-sample z-test. Assuming that the data is based on n = 100: For the two-sample z-test, the test statistic is calculated using the formula:

z = (x1 − x2 − d) / √[s1^2/n1 + s2^2/n2],

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and d is the hypothesized difference between the population means.

In this case, the null hypothesis is that the two population means are equal, so d = 0. The observed difference between the sample means is 60.9 − 60.7 = 0.2. The standard error of the difference between the sample means is: √[1^2/100 + 1^2/100] = 0.1414. Therefore, the test statistic is: z = (0.2 - 0) / 0.1414 = 1.4142.

Solution b) Assuming that the data is based on n = 500: For the two-sample z-test, the test statistic is calculated using the formula:

z = (x1 − x2 − d) / √[s1^2/n1 + s2^2/n2],

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and d is the hypothesized difference between the population means. In this case, the null hypothesis is that the two population means are equal, so d = 0. The observed difference between the sample means is 60.9 − 60.7 = 0.2. The standard error of the difference between the sample means is:

√[1^2/500 + 1^2/500] = 0.0447. Therefore, the test statistic is: z = (0.2 - 0) / 0.0447 = 4.4843.

Solution c)  This is because the p-value is less than the significance level of 0.05, which means that we can reject the null hypothesis and conclude that the two population means are not equal.

Solution d) A statistical conclusion should also be made based on the p-value. In this case, we can conclude that the true average fracture toughness values of the two types of steel are not equal.

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a. (H0): p = 0.50 (the politician is supported by exactly 50% of voters). (H1): p > 0.50 (the politician is supported by more than 50% of voters).

b. Sample proportion = 42/70 = 0.60 (or 60%).

c. Test statistic = (0.60 - 0.50) / sqrt(0.50 * (1 - 0.50) / 70) ≈ 1.61

d. The value and conclusion cannot be determined without knowing the chosen significance level (α) or having information about the critical value or p-value associated with the test statistic.

a. The null hypothesis (H0) in this case would be P = 0.50, indicating that the politician is supported by exactly 50% of the voters. The alternative hypothesis (Ha) would be p ≠ 0.50, suggesting that the proportion differs from 50%.

b. To calculate the sample proportion, we divide the number of voters supporting the politician (42) by the total number of voters surveyed (70):

Sample proportion (p) = 42/70 = 0.60 (rounded to 2 decimal places).

c. The test statistic (z) can be computed using the formula:

z = (p - P) / √(P(1 - P) / n),

where p is the sample proportion, P is the null hypothesis proportion, and n is the sample size. In this case, P = 0.50 and n = 70. Substituting these values, we have:

z = (0.60 - 0.50) / √(0.50(1 - 0.50) / 70) = 2.26 (rounded to 2 decimal places).

d. To determine the value of the test statistic, we compare the computed test statistic (z = 2.26) with the critical values corresponding to the chosen level of significance (e.g., 0.05). By comparing the test statistic with the critical values from a standard normal distribution table, we can evaluate the statistical significance of the results and make conclusions about the claim made by the politician.

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Answer:

First option

Step-by-step explanation:

The "x" side represents a cathetum and is adjacent to the 30-degree angle and the side AC=50 represents hypotenuse

applies the cosine ratio

\(cos30=\frac{x}{50}\)

cos 30° is a noticeable angle that can be expressed as \(\frac{\sqrt{3} }{2}\)

Then:

\(x=50cos30=50(\frac{\sqrt{3} }{2} )=25\sqrt{3}\)

Hope this helps

The values of the gradient and y-intercept of the function is obtained. The graph above shows all the 4 plans in the same graph.

(a) If y is the charges of the plan and x is the number of hours spent on calls, the gradient and y-intercept of the function for each plan are given below:

Plan 1: A flat fee of $50 per month for unlimited calls Gradient: 0,

Y-intercept: 50

Plan 2: A $30 per month fee for a total of 30 hours of calls and an additional charge of $0.01 per minute for all minutes over 30 hours.

Gradient: 0.0003, Y-intercept: 30

Plan 3: A $5 per month fee and a charge of $0.04 per minute for all calls.

Gradient: 0.04, Y-intercept: 5

Plan 4: A charge of $0.05 per minute for all calls: there is no additional fees.

Gradient: 0.05, Y-intercept: 0

(b) The equation of the function for each plan is given below:

Plan 1: y = 50

Plan 2: y = 0.0003x + 30

Plan 3: y = 0.04x + 5

Plan 4: y = 0.05x

Using functions created in Question 1, we can plot a graph using EXCEL to show all the 4 plans in the same graph.

The suitable range of the x-axis is 0 to 100 hours with the interval of 5 hours and the y-axis has the suitable range as 0 to 65 dollars with the interval of 5 dollars.

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Answer:

71. 8

Step-by-step explanation:

volume of a cylinder = 4/ 3 π r² h

=> 4817 = 4/ 3 × 22/ 7 × 4² × h

=> h = (4817 × 3 × 7)/ (4 × 22 × 4²)

=> h = 71.8

Answer:(4,-25)

Step-by-step explanation:

100°

Supplementary angle pairs sum to 180°.

Supplementary Angles

Supplementary angle pairs form a straight line. Since straight lines have a measure of 180°, the sum of supplementary angles is always 180°. Supplementary angles do not necessarily have to be adjacent, but the angles above are. Since the angles above create a straight line together, they must be supplementary angles.

Solving for j

Now that we know that the sum must be 180°, we can create an equation to find j.

To solve this, all we need to do is subtract 80 from both sides.

Angle j must have a measure of 100°.

Answer:

1) 1,3,5,7

2) I can't really see it, it is blurry. Im sorry

Step-by-step explanation:

The statement is true. If the two nonadjacent angles are formed by two intersecting lines, then the  angles are congruent

When two non-adjacent angles are formed with two intersecting lines then they are called​ opposite angles.

There are some properties of nonadjacent angles:

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Answer:

The answer is Point D could be the image of B, Point E could be the image of C, and Point E could be the image of B.

Step-by-step explanation: The clue is going right and up. We could use this clue and know that the answer is correct. For example, if you start with the point B and move right, and go up we can find that both point E and D can all be the image of B.

The true statements are  Point D could be the image of B, Point E could be the image of C, and Point E could be the image of B.

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Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

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Answer:

y=-5x+9

Step-by-step explanation:

y=-5x+b

y=4 x=1

4=-5(1)+b

9=b

Answer:

0.375

Step-by-step explanation:

0.125 x 3 = 0.375

Answer:

0.375

Step-by-step explanation:

3 x 125

8 x 125

=

375

1000

=

0.375

Other sample problem:

5 = 5×125 = 625 = 0.625

8         8×125         1000

Hope this helps, have a good day :)

Answer:

slope

m=\(\frac{9}{4}\)

best of luck!

Answer:  4 3/8 ≈ 4.38

Step-by-step explanation:

To start off, note that 4 3/8 is a mixed number, also known as a mixed fraction. It has a whole number and a fractional number. We have labeled the parts of the mixed number below so it is easier to follow along.

4 = Whole number

3 = Numerator

8 = Denominator

To get 4 3/8 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction.Step 1: Multiply the whole number by the denominator:

4 × 8 = 32

Step 2: Add the product you got in Step 1 to the numerator:

32 + 3 = 35

Step 3: Divide the sum from Step 2 by the denominator:

35 ÷ 8 = 4.375

That's it folks! The answer to 4 3/8 in decimal form is displayed below:

4 3/8 ≈ 4.38

Answer:

Step-by-step explanation:

a) 3n+3n+3=141, 6n+3=141

b) 6n+3=141, 6n=138, n=23

c) 3n and 3n+3, 3(23) and 3(23)+3, 69 and 72