Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2
pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?

Answer:

+2.718

Step-by-step explanation:

from the question,

the sample size is 12

therefore the degree of freedom,

df = 12 - 1

= 11

alpha = 1 - 0.98

= 0.02

this is because the confidence level is 98%

under the t distribution table, a degree of freedom of 11 and 0.02 alpha level = 2.718

the critical value t* = 2.718

I hope this helps!

Answer:

[tex]\large \boxed{\sf \ \ \ -4x^2+8x-8 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex](f-g)(x)=f(x)-g(x)\\\\=3x-1 - (4x^2-5x+7)\\\\=3x-1-4x^2+5x-7\\\\=-4x^2+8x-8[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

5

Step-by-step explanation:

We know that we have to add all numbers then divide it by how many numbers there are. So, 10 + 6 + 9 + 2 + 0 + 3 = 30.  30/6 = 5.  

Answer:

[tex]\huge\boxed{x=\pm4.5}[/tex]

Step-by-step explanation:

The quadratic formula of

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

[tex]y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81[/tex]

substitute

[tex]x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{x - 1}{x + 5} \times \frac{x + 1}{x - 5} [/tex]

To multiply the fraction, multiply the numerators and denominators separately

[tex] \frac{(x - 1) \times (x + 1)}{(x + 5) \times (x - 5)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] simplify the product

[tex] = \frac{ {x}^{2} - 1 }{ {x}^{2} - 25 } [/tex]

Hope this helps..

Best regards!!

Answer:

since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,

sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft

Answer:

increase of 30

Step-by-step explanation:

1255- 1075 = 180

This is an increase of 180

Divide by the number of numbers which is 6

180 /6 = 30

The mean will increase by 30

Answer:

+30

Step-by-step explanation:

1255- 1075 = 180

180 /6 = 30

Answer:

30 years

Step-by-step explanation:

let the age of Ezekiel be x years

Given

Lily is 14 years older than her little brother Ezekiel

Age of Lily = x + 14 years

Next condition

after 8 years\

age of Ezekiel = x+8

age of Lily = x + 8 +14 = x + 22 years

Given

. In 8 years, Lily will be twice as old as Ezekiel will be then.

Thus,

x + 22 = 2(x+8)

=> x + 22 = 2x + 16

=> 22-16 = 2x -x

=> x = 6

Thus, age of  Ezekiel = 8 years

age of lily = 8+14 = 22 years

sum of their age = 22 + 8 = 30 years      answer.

Answer: 35.9

Step-by-step explanation:

The tree is approximately 35.979 feet tall, computed using the sine rule.

The sine rule in a triangle can be shown as this.

A triangle ABC, with the values of the side BC = a, CA = b, and AB = b, follows the rule by:

(Sin A)/a = (sin B)/b = (sin C)/c.

In the question, we are informed about Tasha who is willing to measure the height of a tree, which grows at an angle of 85° with respect to the ground. Also, we are informed that when Tasha is 80 feet away from the base of the tree, then the angle from the ground to the top of the tree is 25°.

We are asked to find the height of the tree.

We first draw a triangle using the given details, AB being the tree, and C being the point where Tasha is.

We know ∠A = 180° - (∠B + ∠C) {By angle sum property of triangles)

or, ∠A = 180° - (85° + 25°) = 180° - 110° = 70°.

Now, by sine rule, we can say that:

(Sin A)/a = (sin B)/b = (sin C)/c.

or, (Sin 70°)/80 = (sin 85°)/b = (sin 25°)/c,

or, 0.93969262078/80 = 0.42261826174/c {We ignored the middle term as we only need the height of the tree, that is, c}

or, c = 0.42261826174*80/0.93969262078/80

or, c = 35.9792768309.

Therefore, the tree is approximately 35.979 feet tall, computed using the sine rule.

Learn more about the sine rule at

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Answer:

The answer is 20

Step-by-step explanation:

(Edge2020)

Answer:

Its A on edge

Step-by-step explanation:

i took the test. good luck guys!

Answer:

D

Step-by-step explanation:

You can test this out with a number.

try dividing 23 by 8:

you will get 2 remainder 7 which works for the condition.

Note: Whenever you divide a number by x(other number) the remainder will always have to be to less than x:

The only one that applies to this aforementioned condition is 8.

Answer:

D

Step-by-step explanation:

The remainder can never be greater than the number by which it is divided

For example:

n = any number

n / 2 -> The remainder will never be greater than 2 (0 < remainder <2)

n / 3 -> The remainder will never be greater than 3 (0 < remainder <3)

n / 4 -> The remainder will never be greater than 4 (0 < remainder <4)

n / 5 -> The remainder will never be greater than 5 (0 < remainder <5)

n / 6 -> The remainder will never be greater than 6 (0 < remainder <6)

..... etc

Answer:  B. 30

Step-by-step explanation:

When given a secant and a tangent, the formula is:

exterior of secant × secant = tangent²

                     KM   ×    JK     =    LK²

                      10   ×  (JM + 10) = 20²

                            10JM + 100 = 400

                                     10JM = 300

                                         JM =  30

Answer:

0.99379

Step-by-step explanation:

The first thing to do here is to calculate the z-score

mathematically;

z-score = x-mean/SD/√(n)

From the question x = 9.5 ,

mean = 9, SD = 2 and n = 100

Plugging the values we have;

z-score = (9.5-9)/2/√(100) = 0.5/2/10 = 0.5/0.2 = 2.5

So the probability we want to calculate is;

P(z<2.5)

We use the standard table for this

and that equals 0.99379

Answer:

Step-by-step explanation:

Let the first integer be x and the second integer be y. If the first integer is 7 more than 2 times another, then x = 7+2y

The two integers will be y and 7+2y. If the product of both integers is 60, then;

y(7+2y) = 60

7y + 2y² = 60

2y² + 7y -60 = 0

2y²-8y+15y-60 = 0

2y(y-4)+15(y-4) = 0

(2y+15)(y-4) = 0

2y+15= 0 and y-4 = 0

2y = -15 and y = 4

y = -15/2 and 4

Taking the positive integer, y = 4

To get the other integer, we will substitute y = 4 into the equation x = 7+2y;

x = 7+2(4)

x = 7+8

x = 15

Hence the two integrs are 15 and 4

Answer:

Step-by-step explanation:

Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same

Let's get the slope of both equation. For the first equation;

y=(3a+2)x-2

We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2

Similarly for the second line;

2y=(a-4)x+2

Re-writing in the standard format we will have;

y = (a-4)x/2+2/2

y = (a-4)x/2 + 1

The slope of the second line is (a-4)/2

On equating the slope of both lines to get the value of 'a' we will have;

3a+2 = (a-4)/2

Cross multiplying

2(3a+2) = a-4

6a+4 = a-4

Collecting like terms;

6a-a = -4-4

5a = -8

a = -8/5

Hence the value of a is -8/5

Step-by-step explanation:

a. z = 5.5

25 ^( 5.5 - 4 ) = 125

25 ^ (1.5) = 125

125 = 125

z = 5.5

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Answer:  D. 125%

Step-by-step explanation:

An INCREASE of 25% means the original volume (100%) + 25% = 125%

Answer:

[tex]\boxed{125\%}[/tex]

Step-by-step explanation:

[tex]original \: pressure=100\%[/tex]

[tex]increase=25\%[/tex]

[tex]new \: pressure=100\%+25\%=125\%[/tex]

The new pressure will be 125% of the original pressure.

Answer:

When you reflect a shape avross the y-axis, the y-coordinates stay the same, but the x-coordinates turn into its opposites.

Step-by-step explanation:

EXAMPLES:

(3,6)---(reflected over y-axis)--> (-3,6)

(9,2)---(reflected over y-axis)--> (-9,2)

Hope this helped! Brainliest would be really appreciated :)

Answer:

9 sides

Step-by-step explanation:

The formula for number of sides of a polygon with a given central angle

Number of sides = 360°/ central angle

In the above question, we were told that each of the central angles in the polygon ha a measure of 40°

Hence,

Number of sides = 360°/40°

9 sides.

Therefore, the number of sides that polygon in the above question has is 9 sides.

Answer:

[tex]a_{n} = a + 2(n-1)[/tex]

Step-by-step explanation:

[tex]a_{5}= a_{1} + 4d \\4 = -4 +4d\\8= 4d\\d= 2\\\\Therefore \\a_{n} = a_{1} + 2(n-1)[/tex]

Answer:

(x - 2)(x + 2)

Step-by-step explanation:

(x - 2)(x + 2) = x² - (2)² [Since (a - b)(a + b) = a² - b²]

                   = x² - 4

There are two terms in this expression. Therefore, the give term is a binomial.

(2x - 1)(x + 4) = 2x(x + 4) - 1(x + 4) [Distributive property]

                    = 2x² + 8x - x - 4

                    = 2x² + 7x - 4

There are three terms in this polynomial. Therefore, the given polynomial is a trinomial.

(x + 4)(x + 1) = x(x + 1) + 4(x + 1)

                   = x² + x + 4x + 4

                   = x² + 5x + 4

This polynomial is having 3 terms therefore, it's a trinomial.

(m - 4)(m + 1) = m(m + 1) - 4(m + 1)

                     = m² + m - 4m - 4

                     = m² - 3m - 4

Therefore, this polynomial is a trinomial.

Since (x - 2)(x + 2) is a binomial, so this expression doesn't belong to this group.

Answer:

X=18

Step-by-step explanation:

Answer:

x = 18or x = - 20

Step-by-step explanation:

Given

x² + 2x = 360 ( subtract 360 from both sides )

x² + 2x - 360 = 0 ← quadratic in standard form

Consider the factors of the constant term (- 360) which sum to give the coefficient of the x- term (+ 2)

The factors are + 20 and - 18, since

20 × - 18 = - 360 and 20 - 18 = 2 , thus

(x + 20)(x - 18) = 0

Equate each factor to zero and solve for x

x + 20 = 0 ⇒ x = - 20

x - 18 = 0 ⇒ x = 18

Thus the number could be 18 or - 20

Answer:

Step-by-step explanation:

From the information given:

Mean [tex]\overline x = \dfrac{\sum x_i}{n}[/tex]

Mean [tex]\overline x = \dfrac{69+103+126+122+60+64}{6}[/tex]

Mean [tex]\overline x = \dfrac{544}{6}[/tex]

Mean [tex]\overline x = 90.67[/tex] pounds

Standard deviation [tex]s = \sqrt{\dfrac {\sum (x_i - \overline x) ^2}{n-1}[/tex]

Standard deviation [tex]s = \sqrt{\dfrac {(69 - 90.67)^2+(103 - 90.67)^2+ (126- 90.67) ^2+ ..+ (64 - 90.67)^2}{6-1}}[/tex]

Standard deviation s = 30.011 pounds

B) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region.

At 75% confidence interval ; the level of significance ∝ = 1 - 0.75 = 0.25

[tex]t_{(\alpha/2)}[/tex] = 0.25/2

[tex]t_{(\alpha/2)}[/tex] = 0.125

t(0.125,5)=1.30

Degree of freedom = n - 1

Degree of freedom = 6 - 1

Degree of freedom = 5

Confidence interval  = [tex](\overline x - t_{(\alpha/2)(n-1)}(\dfrac{s}{\sqrt{n}})< \mu < (\overline x + t_{(\alpha/2)(n-1)}(\dfrac{s}{\sqrt{n}})[/tex]

Confidence interval  = [tex](90.67 - 1.30(\dfrac{30.011}{\sqrt{6}})< \mu < (90.67+ 1.30(\dfrac{30.011}{\sqrt{6}})[/tex]

Confidence interval  = [tex](90.67 - 1.30(12.252})< \mu < (90.67+ 1.30(12.252})[/tex]

Confidence interval  = [tex](90.67 - 15.9276 < \mu < (90.67+ 15.9276)[/tex]

Confidence interval  =  [tex](74.7424 < \mu <106.5976)[/tex]

i.e the lower limit = 74.74 pounds

    the upper limit = 106.60 pounds

Answer: 64% of the variability in weight can be explained by the relationship with height.

Step-by-step explanation:

Here, r= 0.80

[tex]\Rightarrow\ r^2= (0.80)^2=0.64[/tex]

That means 64% of the variability in weight can be explained by the relationship with height.

The variability in weight is 64 % , explained by the relationship with height.

Correlation coefficients are always values between -1 and 1, where -1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation.

The correlation coefficient is measure the strength of the linear relationship between two variables in a correlation analysis.

Correlation coefficient is represented by r.

Given that, the correlation between height and weight for adults is 0.80.

                   [tex]r=0.8[/tex]

The variability in weight is, = [tex]r^{2}=(0.8)^{2} =0.64[/tex]

Thus, the variability in weight is 64 % , explained by the relationship with height.

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Complete Question

Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.

Answer:

The  sample size is  [tex]n = 1537 \ gallons[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]MOE = 0.5[/tex]

     The confidence level is  [tex]C = 95[/tex]%

Given that the confidence level is  95% the level of significance is mathematically represented as

         [tex]\alpha = 100 - 95[/tex]

         [tex]\alpha = 5[/tex]%

         [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is  [tex]Z_{\frac{\alpha }{2} } = 1. 96[/tex]

The reason we are obtaining critical values of  

[tex]\frac{\alpha }{2}[/tex]

instead of  

[tex]\alpha[/tex]

is because  

[tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (

[tex]1-\alpha[/tex]

) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex]

is just the area of one tail which what we required to calculate the sample size

Now the sample size is mathematically represented as

          [tex]n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}[/tex]

substituting values

         [tex]n = \frac{1.96^2 * 10 ^2}{0.5^2}[/tex]

         [tex]n = 1537 \ gallons[/tex]

Answer:

Step-by-step explanation:

Let the length of first piece be L .

Length of second piece = 56 - L

radius of circle made from first piece

R = L / 2π

Area of circle = π R²

= L² / 4π

side of square made fro second piece

= (56 - L) / 4

area of square = ( 56-L)² / 16

Total area

A = L² / 4π + ( 56-L)² / 16

For smallest possible combined area

dA / dL = 0

dA / dL = 2L /  4π - 2( 56-L)/16 =0

2L /  4π = 2( 56-L)/16

.159 L = 7 - .125 L

.284 L = 7

L = 24.65 inch

other part = 56 - 24.65

= 31.35 inch .

Answer:

Step-by-step explanation:

Using the formula for calculating the energy used up during the process;

Energy used up = Amount of CO₂ created.

Energy used up in the process = Power * Time.

Given Parameters:

Power = 3,030Watts

Converting to Kilowatts, power = 3030/1000 kW

Power (in kW) = 3.03kW

Time taken = 34 minutes

Converting to hour;

Since 60 minutes = 1hr

34minutes = (34/60)hr

34minutes = (17/30)hr

Required:

Energy used up = 3.03 * 17/30

Energy used up = 51.51/30

Energy used up = 1.717 kW/hr

Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.

Answer:

The central angle for the cheese sector would be 108 degrees.

Step-by-step explanation:

We know that a pi chart takes the form of a circle so the total angle measure is 360 degrees.

Now we want to find out what ratio of the pie chart that cheese takes up and apply it to the total degree measure.

30 of 100 students voted for cheese:

so the ratio would be 30/100 or 3/10

Now apply that to the total angle measure:

3/10*360 degrees= 108 degrees.

Answer:

x > 29

Step-by-step explanation:

−x<−29

Divide each side by -1, remembering to flip the inequality

x > 29

Answer:

Step-by-step explanation:

-x < -29   change the signs

x > 29

Answer:

Step-by-step explanation:

PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

We have to do operations by the Order of Operations(PEMDAS)

Parentheses:

           Addition/Subtraction:

            (7 - 1)

             (6)

16/4 + 56 - 6

Multiplication/Division

4 + 56 - 6

Addition/Subtraction

60 - 6