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2 years ago

HELP DUE IN AN HOUR

Mathematics

2 answers:

Alexeev081 [22]2 years ago

7 0

Answer:

no solution. not 100% sure though

miss Akunina [59]2 years ago

4 0

Answer:

D) no solution.

Step-by-step explanation:

4(x + 1) ≤ 4x + 3

First, distribute 4 to all terms within the parenthesis:

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

4x + 4 ≤ 4x + 3

Isolate the variable, x. Treat the "≤" as an equal sign, what you do to one side, you do to the other. Subtract 4x and 4 from both sides:

4x (-4x) + 4 (-4) ≤ 4x (-4x) + 3 (-4)

4x - 4x ≤ 3 - 4

0 ≤ -1

Since x was eliminated from the inequality, and you need the x for the inequality, your answer is D) no solution.

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Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile

Llana [10]

Answer: 37

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.98=0.02$

Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

margin of error : E= 1 mile per gallon

Population standard deviation: $\sigma=2.6$ miles per gallon.

We know that when the population standard deviation is known then the formula to find the sample size is given by :

$n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2$

$n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37$ [Round to the next whole number.]

Hence, the required number of automobiles should be used in the test = 37

7 0

3 years ago

A mother has two children whose ages differ by 5 years. The sum of the squares of their ages is 97. The square of the mother's

svetoff [14.1K]

Answer:

41 years old.

Step-by-step explanation:

Let x represent age of younger child.

We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be $x+5$ .

The sum of the squares of their ages is 97. We can represent this information in an equation as:

$x^2+(x+5)^2=97$

Let us solve for x.

$x^2+x^2+10x+25=97$

$2x^2+10x+25-97=0$

$2x^2+10x-72=0$

Divide both sides by 2:

$x^2+5x-36=0$

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x+9)(x-4)=0$

$(x+9)=0 ; (x-4)=0$

$x=-9 ; x=4$

Since age cannot be negative, therefore, age of younger child is 4 years.

Age of older child would be $x+5\Rightarrow4+5=9$

Therefore, the age of older child would be 9 years.

We have been given that the square of the mother's age can be found by writing the squares of the children's ages one after the other as a four-digit number.

Square of 4: $4^2=16$

Square of 9: $9^2=81$ .

Square of mother's age: $1681$

To find mother's age, we need to take positive square root of 1681 as:

$\sqrt{1681}=41$

Therefore, the mother is 41 years old.

4 0

3 years ago

Which of the following has a value of 84? <br> A. 512 <br> B. 4,096 <br> C. 32 <br> D. 83

andreev551 [17]

Answer is B. 4,096

I encountered this problem before. This is a trick question.
84 is not really the number 84. It is 8 raised to the 4th power.

So 8⁴ is equal to 4,096.

8 x 8 x 8 x 8 = 4,096

8 x 8 = 64
64 x 8 = 512
512 x 8 = 4,096

6 0

3 years ago

Justine is planting flowers in a line that is 1/2 of a yard long. She is going to plant 6 flowers. How far apart will each flowe

erica [24]

Answer:

3 inches apart

Step-by-step explanation:

1/2 yard is 1ft. 6in. in decimal that is 1.5 ft

1.5 ÷6 = 0.25ft

0.25ft is 3 inches so the answer is three inches apart

6 0

3 years ago

What is the formula for the circumference of a circle?

Juli2301 [7.4K]

Answer:

C = pi * d = 2 * pi *r

Step-by-step explanation:

The circumference of a circle is the distance around the circle. It can be found by multiplying the diameter times pi.

C = pi * d

We can replace the diameter with twice the radius

C = pi * 2 * r = 2 * pi *r

5 0

3 years ago