Use the properties of operations to multiply the expressions. (10.3y)(4y)

a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)

b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.

Given:

Confidence level,c = 90% = 0.90

Number of successes, x = 153

Sample size,n = 434 + 153 = 587

a) The sample proportion is the number of successes divided by the sample size is,

p = x/n

p = 153/587

p ≅ 0.2606

For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix

[tex]z_{\alpha /2} = 1.64[/tex]

The margin of error is calculated as:

[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]

E ≅ 0.0297

Therefore, the boundaries of the confidence interval are:

p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%

p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%

We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.

b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.

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Answer:

Smallest to largest would be:

0.008, 0.086, 0.867, 0.870

Step-by-step explanation:

math.

it is vital that we first find the gradient/slope between the points .

⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]

The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.

[tex]2=-2(0)+c\\\\c=2[/tex]

⇒This tells us that the equation of the line is y=-2x+2

Ths values of a and b in the equivalent ratio illustrated on the table will be 6 and 12

It should be noted that from the information given, the relationship that exist between the numbers is illustrated as:

y = 0.8x

Therefore, when y is 4.8, the value of x will be:

y = 0.8x

x = 4.8 / 0.8

x = 6

When x = 15, the value of y will be:

y = 0.8x

y = 0.8 × 15

y = 12

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Answer:

There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul

Step-by-step explanation:

In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.

Firstly, we shall calculate the z score

Mathematically;

z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35

so we are to calculate the probability of; P(z< -2.35) = 0.0094

This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{2}\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 2^2}\implies c=\sqrt{16 + 4}\implies c=\sqrt{20}[/tex]

For the given expression (8^7)^2 = 2^y , the number equals to y is 42.

As given in the question,

Given expression :

(8⁷)² = [tex]2^{y}[/tex]

Simplify the given expression by using law of exponents :

Here the law of product of exponents or product law of exponents (power or index) has been applied under which [tex](8^{7})^{2} = 8^{7times2} = 8^{14}[/tex]

(  8¹⁴ ) =  [tex]2^{y}[/tex]

⇒ (2³)¹⁴ = [tex]2^{y}[/tex]

⇒ 2⁴² =  [tex]2^{y}[/tex]

Comparing the exponents i. e. power (or index), since the base is common, Also when two exponential numbers with common base are equal, their exponents (power or index) can be equated.

Number equals to represent the value of y is 42

Therefore, for the given expression (8^7)^2 = 2^y , the number equals to y is 42.

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The most appropriate choice for corrosponding angle will be given by-

x = 2 is the correct answer

What is corrosponding angle?

At first we need to understood what is angle, parallel lines and transversal

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Parallel lines

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal

Transversal is a line that intersects two or more parallel lines

Corrosponding angle

The angles formed in the same position on the same side of transversal when a transversal cuts two or more parallel lines

Here,

(7x + 3)° and (8x + 1)° are corrosponding angles.

Lines m and n are parallel.

So corrosponding angles are equals

By the problem,

(7x + 3) = (8x + 1)

8x - 7x = 3 - 1

x = 2

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The lengths 8 cm, 14 cm, 15 cm can form a triangle

Given 8 cm, 14 cm, 15 cm

These can form a triangle if the sum of any two sides of the triangle is greater than the third side.

8 + 14 > 15

14 + 15 > 8

8 + 15 > 14

Since all the above are true, we conclude that they can form a triangle

The width of rectangle is 83 meter.

What is the area of rectangle?

By dividing the rectangle's length by its breadth, we may determine the area of a rectangle.

Formulas for rectangles.

Formula for the perimeter of a rectangle. Rectangle Area Formula: P = 2 (l + b). A = l × b, where l is length of rectangle and b is width of rectangle.

Given area of rectangle is 8217m^2

length l = 99 m

Let width of rectangle be b meter

Therefore,

99 x b = 8217

=> b = 8217/99

=> b = 83

Therefore, the width of rectangle is 83 m.

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Answer:

Step-by-step explanation:

x=3?

Answer:

3

Step-by-step explanation:

If you multiply 1 by 3 it gives you 3, the side of triangle B. Using that scale factor. you can then take the side of triangle B that is 9 and divide it by 3. That gives you the missing side of triangle A.

Hope this helps! :)

We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root

[tex]x-7\geq 0\\x\geq 7[/tex]

The domain of the function is all the real numbers greater or equal to  7 .

x≥7 ε R

[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]

ATTACHED IS THE SOLUTION

Step-by-step explanation:

-4+8=4

-23+-1=-24

this is correct answer

Answer: [tex]72z^{2} +55z-7[/tex]

Step-by-step explanation:

We multiply each component with each other:

8z * 9z = 72z^2

8z * -1 = -8z

9z * 7 = 63z

7 * -1 = -7

We then add it all together, 63z + -8z = 55z and get

[tex]72z^{2} +55z-7[/tex]

The sum of mAB and mBC is equal

360 - mAC

which makes otion A the correct answer

Equation for the function graphed is f(x) = -0.6 (x - 1)² ÷ (x + 1)(x + 3)

Given, the y-intercept is at (0, 0.2).

From the given graph, it can be deduced the vertical asymptotes are at x = -1, x = 1 and x = -3.

Which implies denominator is 0 and the function is undefined for x = -1, x = 1 or x = -3.

So, -1 and -3. are the roots of the denominator. As a result, the denominator equation has the form: (x + 1)(x + 3).

For finding the equation of the function f(x) = a(x - 1)² ÷ (x + 1)(x + 3)

Put f(0) = 0.2

f(0) = a(0 - 1)² ÷ (0 + 1)(0 + 3) = 0.2

a = - 0.6

∴ Equation is f(x) = -0.6(x - 1)² ÷ (x + 1)(x + 3) for y-intercept is at (0,0.2).

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Answer:

18 more tickets

Step-by-step explanation:

What we know:

We know that 65 Tickets is 1 Prize.

We know we have 1,282 tickets.

So if 65 tickets is one prize

then to figure out how many for twenty then we:

65 x 20 = 1300

Now to figure out how many more she needs at the least we:

1300 - 1282 = 18

So for 1 more prize she needs 18 more tickets.

The equation written in exponential form is (a) 2³ = 8

A symbol used to denote the action of raising to a power that is written above and to the right of a mathematical phrase.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

㏒₂ 8 = 3

㏒ₐx = b

x = aᵇ

㏒₂8 = 3

8 = 2³

Hence, (a) 2³ = 8

Therefore, the equation written in exponential form is (a) 2³ = 8.

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Answer:

221 760 inches

Step-by-step explanation:

So, 3.5miles * 63360= 221760 inches.

Formula: multiply the value in miles by the conversation factor '63360'.

Answer:

C

Step-by-step explanation:

multiply 24.23 by 4

Answer:

74.44

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]

Given:

The matrics

Required:

Match lettered entries in the matrices A, B and AC to their values.

Explanation:

First multiply matrices A with B

Now we can find values of a, b, c, d, e and f from equating two matrices as:

Answer:

The values are a = 2, b = 12, c = -1, d = -3, e = 5 and f = 19.

Answer:

[tex]y=-\frac{4}{3}x+3[/tex]

The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.

[tex](1+10)^{15}[/tex]Venus invests $1,200 per year and stops after 15 years.

He can get money : [tex]1200*[/tex] [tex](1+10)^{15}[/tex] at the first year,

We can use ,

Compound interest formula, S = [tex]P*(1+i)^{n}[/tex]

Where,

P means the Principal

I means the interest

n means the year

S means the principal and interest

At the second year he can get,

= 1200 * [(1+[tex]\frac{10degrees}{1}[/tex]) + ([tex]1+[\frac{10degrees}{1} ]^{2}[/tex])

The money of first year has two years interest,

The money of second year has one year interest.

So, we can calculate the 15th year he can get :

= 1200 * [[tex](1+\frac{10degrees}{1}] ^{1}) +(1+(\frac{10degrees}{1} )^{2} )+......(1+(\frac{10degrees}{1})^{15} )[/tex]

= 1200 * [tex]\frac{(1*1)*(1-1*1^{15} )}{1-1*1}[/tex]

The sum of geometric progression,

[tex]S_{n} =\frac{a*(1-q)^{n} }{1-q}[/tex]  ,  q≠1

= $ 41939.67

The rest of years he can get money :

= 41939.67 * ([tex](1+10percent))^{40-15}[/tex]

= $ 454404.053

Kevin can get money 1200* [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{15} )[/tex]

= 41939.67 at 30th year

Finally he can get money = 41936.67 [tex](1+\frac{10degrees}{1}) ^{40-15*0}[/tex]

= $ 108780.71

Rafael can get money : 1200 * [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{25} )[/tex]

= $ 129818.11

$454404.05 > $129818.11 > $108780.71

Therefore,

The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.

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The logarithmic function log ( x³ y² ) when expressed in terms of log x and log y is 3 log ( x ) + 2 log( y).

The opposite of exponentiation is the logarithm. In other words, the exponent to which a fixed number, the base a, must be raised in order to create a specific number x, is represented by the logarithm of that number.

Consider the logarithmic function log x³ y⁴

Using the logarithmic formula,

log ( a b ) = log  (a) + log (b)

We have,

log( x³ y² )  = log ( x³ ) + log( y² )

By applying the logarithmic property:

log ( xⁿ ) = n log x

We have,

log x³ y² = log ( x³ ) + log( y² )

log x³ y² =  3 log ( x ) + 2 log( y)

Therefore, the function log ( x³ y² ) in terms of log x and log y is 3 log ( x ) + 2 log( y).

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Answer:

[tex]1. a=-10[/tex]

[tex]2. b=-0.2[/tex]

[tex]3. c=0.25[/tex]

Step-by-step explanation:

1. 1/5a = -2

a=-10

2. 8+b=7.8

b=-0.2

3.-0.5=-2c

c=0.25

:]

(Brainliest would help a lot) Tell me if this is incorrect!

Answer:

GH = 2

Step-by-step explanation:

since F is the midpoint of EG , then EF = FG = 4

EF + FG + GH = EH , that is

4 + 4 + GH = 10

8 + GH = 10 ( subtract 8 from both sides )

GH = 2

Answer:

a

Step-by-step explanation:

as all the other points had inflection

a. Given the expression of the form Ax + By + C = 0, the slope is

In this case: A = -2 and B = 3.

Answer: 2/3

b. A = -4 and B = 1, so

Answer: 4

c. A = 5 and B = -7, so

Answer: 5/7

d. A = 5 and B = -8, so

Answer: 5/8