For the following right triangle, find the side length x. Round your answer to the nearest hundredth. 11, 19

Answer:

[tex]\large\boxed{x^2+4x+3=(x+3)(x+1)}[/tex]

Step-by-step explanation:

[tex]x^2+4x+3\\\\\text{We are looking for a and b, for which a + b = 4 and (a)(b) = 3}\\\\\text{a=3,\ b=1}\\\\=x^2+3x+1x+3\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=x\underbrace{(x+3)}_{(*)}+1\underbrace{(x+3)}_{(*)}\qquad\text{use the distributive property}\\\\=\underbrace{(x+3)}_{(*)}(x+1)[/tex]

Answer:

[tex]9) \$1236.27\,10)\,\$6451.07\, 11)\,\$10,152.87 \,12)\,\$907.95 \,13)\,\$4957.69[/tex]

Step-by-step explanation:

9) Since Alicia Martin's savings earns 6% quarterly for two quarters then:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] ⇒ Amount (A), Principle (P), rate (r) in decimal form, number of compoundings (n) a year and t, in year or its fractions.

[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=1200(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A=\$1236.27[/tex]

10) Aubrey Daniel's case:

[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=5725(1+\frac{0.04}{4})^{4*3}\Rightarrow A\approx \$6451.07[/tex]

11) As for Angelo, similarly to Alicia.

[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=9855(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$10,152.87[/tex]

12) Simpson's. For semiannual n=2

[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=860(1+\frac{0.055}{2})^{2*1}\Rightarrow A\approx \$907.95[/tex]

13) Jana Lacey amount:

[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=4860(1+\frac{0.04}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$4957.69[/tex]

Answer:

4712.39(2 decimal place)

Step-by-step explanation:

Volume of cylinder is πr^2(h)

π10^2(15):

is 4712.39(2dp)

Answer:

1500π

Step-by-step explanation:

The volume of water is just the normal volume so,

the volume of a cylinder is πr²h

where π is pi, as in 3.14 ..., r is the radius, and h is the height.

Using what was given to us, we can plug this into the formula

so, π ×10² ×15 = 100π×15 = 1500π

Answer:

27 / (4x⁶y⁸)

Step-by-step explanation:

[tex]\frac{4(3x^{2}y^{4})^{3}}{(2x^{3}y^{5})^{4}}[/tex]

When raised to a power, multiply the exponents.

[tex]\frac{4(3^{3}x^{6}y^{12})}{2^{4}x^{12}y^{20}} \\\\\frac{2^{2}3^{3}x^{6}y^{12}}{2^{4}x^{12}y^{20}}[/tex]

When dividing, subtract the exponents.

[tex]2^{2-4}3^{3}x^{6-12}y^{12-20}\\2^{-2}3^{3}x^{-6}y^{-8}[/tex]

Move negative exponents to the denominator.

[tex]\frac{3^{3}}{2^{2}x^{6}y^{8}}\\\frac{27}{4x^{6}y^{8}}[/tex]

Answer:

Let x = (the height of the fourth plant)

Then the average of the four heights will be:

(70+71+72+x)/4

Simplify it to (213+x)/4

This average has to be at least 73 inches. Meaning, it has to be greater than or equal to 73.

(I don't have the sign for greater/equal so I'll type >=)

(213+x)/4 >= 73

This is the inequality. Just solve for x, and you have the answer.

(213+x) >= 292

x >= 79

Another way: (I think it's easier to do it like this in my head)

You need average 73.

Look at the heights of the plants you have now: how far are they from 73?

The first is 3 less, the second is 2 less, and the third is 1 less.

The 'total deficit'' is 6.

So to make the average be 73, you need to cancel out the deficit by making an equal overage (by 6).

If you can only add one more plant... that plant has to be 6 inches higher than the average you want. So 73+6=79.

Step-by-step explanation:

Answer:

m∠HMO=102°

Step-by-step explanation:

we know that

In a Rhombus the diagonals bisect the angles and opposite angles are equal

In this problem

Angles HMO and HTO are opposite angles

m∠HMO=m∠HTO

m∠HTM=(1/2)m∠HMO ----> because the diagonals bisect the angles and opposite angles are congruent

substitute the values

[tex](5x+6)\°=(1/2)(12x-6)\°[/tex]

solve for x

[tex]10x+12=12x-6\\12x-10x=12+6\\2x=18\\x=9[/tex]

Find the measure of angle HMO

m∠HMO=(12x-6)°

substitute the value of x

m∠HMO=(12(9)-6)=102°

see the attached figure to better understand the problem

Answer:

D - 9x^(2)+2x-5

Step-by-step explanation:

Answer:

[tex]\large\boxed{y=\dfrac{7}{2}x-2}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the point (4, 12), and y-intercept b = -2 → (0, -2).

Substitute:

[tex]m=\dfrac{-2-12}{0-4}=\dfrac{-14}{-4}=\dfrac{14:2}{4:2}=\dfrac{7}{2}[/tex]

Finally:

[tex]y=\dfrac{7}{2}x-2[/tex]

Final answer:

To calculate the total movie-going cost for five friends, multiply the cost of each item by five and sum them up. The total cost is represented by the expression [tex](5 \times\$9) + (5 \times\$3) + (5 \times\$6)[/tex], which simplifies to $90.

Explanation:

The question involves writing an expression to determine the cost for five friends to attend a movie considering the cost of tickets, drinks, and popcorn. To calculate the total cost for the group, we need to know the price per individual item and the quantity consumed. We know that each ticket costs $9, each drink costs $3, and each popcorn costs $6. Since there are five friends, we will multiply each of these costs by five to get the total cost per item for the group.

The expression for the total cost for the movie tickets is [tex]5\ tickets \ \times \$9/ticket[/tex], for drinks it's [tex]5\ drinks\ \times\$3/drink[/tex], and for popcorn, it's [tex]5\ popcorns \times\$6/popcorn[/tex]. To find the overall total, we add these expressions together:

Total Cost = [tex](5 \times\$9) + (5 \times\$3) + (5 \times\$6)[/tex]

The expression simplifies to:

Total Cost = ($45) + ($15) + ($30)

Therefore, the simplified expression for the total cost is:

Total Cost = $90

Option D. 2(n + 9) is the right answer

Step-by-step explanation:

The word problems are converted into mathematical problems to solve simply.

for the given problem

"two times the sum of a number and 9"

Let n be a number then

when there is and between two things they are performed first then next operation is performed so

the sum of a number and 9

[tex]n+9[/tex]

Then

two times the sum of a number and 9

[tex]2(n+9)[/tex]

Hence,

Option D. 2(n + 9) is the right answer

Keywords: Mathematical notation

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Final answer:

The correct expression is '2(n + 9),' which corresponds to choice D and represents two times the sum of a number and 9.

Explanation:

The expression that represents the statement 'two times the sum of a number and 9' is D. 2(n + 9). This is because you first need to find the sum of the number (let's call it n) and 9, which is represented as (n + 9). Then, the statement says 'two times' which means you need to multiply that sum by 2, resulting in 2 × (n + 9).

Answer:

1/2

Step-by-step explanation:

both have equal chances

The required probabilities are 3/8 and 1/8 respectively.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Jackie has 6 skirts and 2 dresses.

Total number of dresses=8

Thus the probability of picking a skirt is = 6/8

                                                                   =3/4

And the probability of picking a dress is =2/8

                                                             =1/4

Also, the probability of choosing either shoe is 1/2

Therefore the conditional probability that she chooses a skirt and brown shoes is = 3/4×1/2

              =3/8

Similarly Probability( dress+black shoes)=1/4×1/2

                                                                   =1/8

Hence, The required probabilities are 3/8 and 1/8 respectively.

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Answer:

x=1

Step-by-step explanation:

use distributive property for the negative 5, then simplify, then bring the 15 to the other side, then divide by 3. picture included.

Answer:

x = -2

y = 4

Step-by-step explanation:

Given

[tex]-10x+12i=20+3yi[/tex]

Two complex numbers are equal when they have equal real and imaginary parts.

Equate real parts:

[tex]-10x=20\\ \\x=-\dfrac{20}{10}=-2[/tex]

Equate imaginary parts:

[tex]12=3y\\ \\y=\dfrac{12}{3}=4[/tex]

Final answer:

The values of x and y that satisfy the given complex equation are x = -2 and y = 4, found by equating the real and imaginary parts respectively.

Explanation:

To find the values of x and y that satisfy the equation -10x + 12i = 20 + 3yi, we need to equate the real parts and the imaginary parts of the complex numbers on both sides of the equation.

For the real parts, we have:
-10x = 20
=> x = -2

For the imaginary parts, we have:
12 = 3y
=> y = 4

So the solution for the equation is x = -2 and y = 4.

4. 3x + 2y = 6

x-intercept = 2 ,  y - intercept = 3

5. 4x – 9y = 36

x-intercept = 9, y - intercept = -4

6. x + y = -3

x-intercept = -3, y - intercept = -3

8. x - 3y = 12

x-intercept = 12, y - intercept = -4

Step-by-step explanation:

To find the x-intercept we put y=0 in the equation and to find the y-intercept we put x = 0 in the equation

4. 3x + 2y = 6

Putting y = 0

[tex]3x + 2y = 6\\3x +2(0) = 6\\3x = 6\\\frac{3x}{3} = \frac{6}{3}\\x= 2[/tex]

Putting x=0

[tex]3x + 2y = 6\\3(0) + 2y = 6\\2y = 6\\\frac{2y}{2} = \frac{6}{2}\\y= 3[/tex]

5. 4x – 9y = 36

Putting y = 0

[tex]4x -9y = 36\\4x - 9(0) = 36\\4x = 36\\\frac{4x}{4} = \frac{36}{4}\\x = 9[/tex]

Putting x=0

[tex]4(0) -9y = 36\\-9y=36\\\frac{-9x}{-9} = \frac{36}{-9}\\x =-4[/tex]

6. x + y = -3

Putting y = 0

[tex]x+y=-3\\x+0 = -3\\x = -3[/tex]

Putting x=0

[tex]x + y = -3\\0+y=-3\\y=-3[/tex]

8. X - 3y = 12

Putting y=0

[tex]x - 3(0) = 12\\x -0 = 12\\x = 12[/tex]

Putting x = 0

[tex]0-3y = 12\\-3y = 12\\\frac{-3y}{-3} =\frac{12}{-3}\\y=-4[/tex]

Keywords: Linear equation

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Answer:

$1.20 per chicken wing

Step-by-step explanation:

15 chicken wings = $18

1 chicken wing = $18/15 = $6/5 = $1.20

Answer:

1/1000 or 1x10^(-3)

Step-by-step explanation:

0.001=1/1000 as a fraction

With a negative exponent?

You can write it into standard notation.

It's 1x10^(-3).

0.001 as a fraction with a negative exponent is 10⁻³.

To express the decimal 0.001 as a fraction with a negative exponent, we need to understand how negative exponents work with powers of ten. The decimal 0.001 is equivalent to the fraction [tex]\frac{1}{1000}[/tex], which can be written as [tex]\frac{1}{103}[/tex].

Using the concept of negative exponents, [tex]\frac{1}{103}[/tex] can be rewritten as 10⁻³. This is because a negative exponent indicates the inverse of the corresponding positive exponent. So, 0.001 = 10⁻³.

Summary in Steps:

Therefore, 0.001 equals 10⁻³ as a fraction with a negative exponent.

The water should fill the aquarium to 1.5 feet

Solution:

Given that the directions for the aquarium say that it should be filled with 9 cubic feet of water.

This means volume of aquarium is 9 cubic feet

Given that aquarium is 2 feet wide and 3 feet long

To find: Height of aquarium

Since a aquarium is in shape of cuboid, we can use the volume of cuboid formula

The volume of cuboid is given as:

volume of cuboid = [tex]l \times w \times h[/tex]

Where "l" is the length

w is the width

"h" is the height

Substituting the values, we get,

[tex]9 = 3 \times 2 \times h\\\\9 = 6 \times h\\\\h = \frac{9}{6} = 1.5[/tex]

Thus the height of aquarium is 1.5 feet

Answer:

[tex]\sin \theta=-\frac{4}{5}[/tex]

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse = [tex]\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Now, using the sine ratio for the angle, we have

[tex]\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}[/tex]

Therefore, the value of [tex]\sin \theta[/tex] is [tex]-\frac{4}{5}[/tex].

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

The expression which is equivalent to the given expression; 2(3a+2b−7) is; 6a +4b -14

The given expression is;

Upon expansion by multiplying all elements in the parenthesis by 2; we have;

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Final answer:

By distributing the 2 across each term in the expression 2(3a+2b-7), the equivalent expression is 6a + 4b - 14, which corresponds to answer choice D.

Explanation:

To determine which expression is equivalent to 2(3a+2b-7), we need to distribute the 2 across each term in the parentheses. This means we'll multiply 2 by 3a, 2b, and -7 separately. Here's the step-by-step distribution:

Combining these results, we get the equivalent expression: 6a + 4b - 14, which matches answer choice D.

Answer:

about 0.46 cents per ounce

Step-by-step explanation:

5.99 divided by 13 gives you a long decimal and you round to 0.46

[tex]\bf \begin{array}{ccll} inches&cents\\ \cline{1-2} 17&51\\ 33&x \end{array}\implies \cfrac{17}{33}=\cfrac{51}{x}\implies 17x=33\cdot 51\implies x = \cfrac{33\cdot 51}{17} \\\\\\ x = 33\cdot \cfrac{51}{17}\implies x = 33\cdot 3\implies x = 99[/tex]

Final answer:

To find the cost of 33 inches of wire, we calculate the cost per inch from the given 17 inches costing 51 cents, which is 3 cents per inch, and then multiply by 33 inches to get a total cost of 99 cents.

Explanation:

The student is asking to determine the cost of 33 inches of wire based on the given rate of 17 inches costing 51 cents. To solve this, we can set up a proportion where we compare the given inches of wire to the given cost and then find the cost for the desired inches of wire.

Step-by-Step Calculation:

First, we determine the cost per inch of wire by dividing the total cost by the total length of wire: 51 cents ÷ 17 inches = 3 cents per inch.

Next, we multiply the cost per inch by the desired length of wire to find the total cost: 3 cents/inch × 33 inches = 99 cents.

Therefore, 33 inches of wire will cost 99 cents at the same rate.

Answer:

Step-by-step explanation:

Option C is the most reasonable answer, because there's no way that the color of the house affects the homeowners insurance premium.

A homeowners insurance premium refers to a monthly or annual payment to an insurance company which maintain the house and stuff insured. This amount can be variate depending on the size, location and age of the home, but not depends on the color of it.

Answer:

4.6875 is the answer

Step-by-step explanation:

First, lets put both into just ounces. (1lb = 16oz.)

8lb. 1oz. = 129oz.

3lb. 6oz. = 54oz.

Second, subtract.

129 - 54 = 75

Third, put into pounds and ounces.

75oz. = 4lb. 11oz.

_______

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Answer:

Cell division

Step-by-step explanation:

During the process where the cell splits, it’s going through a process of cell division where the cell divides into two

We are testing the claim that males speak fewer words than females. With a p-value of 0.369, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, no significant evidence supports the claim that males speak fewer words than females.

The objective here is to test the claim that on average, males speak fewer words in a day than females. To do this, we compare two means using a hypothesis test for paired data.

The null hypothesis (H0) is that there is no difference between the mean number of words spoken by males and females. The alternative hypothesis (Ha) is that the mean number of words spoken by males is less than that spoken by females.

Since the p-value (0.369) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means we do not have significant evidence to support the claim that males speak fewer words than females.

A key takeaway from this is that the test statistic and p-value are critical elements in hypothesis testing. They determine whether or not you have significant evidence to reject the null hypothesis.

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Answer:

The distance between A and B is l(AB) = 13 units

Step-by-step explanation:

Given:

let,

A ≡ ( x1, y1 ) ≡ ( 0, 12 )

B ≡ ( x2, y2 ) ≡ ( 5, 0 )

To Find:

Length AB = ?

Solution:

Distance Formula for the distance between the two points ( x1, y1 ) and ( x2, y2 ) we have,

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

On substituting the above values we will get,

[tex]l(AB) = \sqrt{((5-0)^{2}+(0-12)^{2} )}\\l(AB)=\sqrt{(5^{2} +(-12)^{2} } \\l(AB)=\sqrt{(25+144)}\\ l(AB)=\sqrt{169} \\l(AB)=13\ unit[/tex]

Therefore the distance between A and B is l(AB) = 13 units

Answer:

Answer:

$30,000 and $55,000

Step-by-step explanation:

If 4.5% loan is x, and the 6% loan is y, then:

x + y = 85000

0.045x + 0.06y = 4650

Solve the system of equations with substitution or elimination.  Using substitution:

0.045x + 0.06(85000 − x) = 4650

0.045x + 5100 − 0.06x = 4650

450 = 0.015x

x = 30000

y = 55000

Loan I = $ 30,000

Loan II = $ 55,000

Total loan of $ 85,000

Loan I rate at 4.5%

Loan II rate at 6%

This year's loan repayments are $ 4,650

0.045 + 0.06 = 4,650

Loan II = $ 85,000 - Loan I

0.045 ($85,000-b)+0.06 b= 4,650

Loan II = $55,000

Loan I = $ 85,000 - Loan II

Loan I = $85,000 - $55,000

Loan I = $30,000

Loan I rate = $ 1,350

Loan II rate = $ 3,300

Total Loans rate (I + II) - Payments = ($ 1,350  + $ 3,300) - $ 4,650 = $ 0 (Remaining balance)

Loans are a type of debt that can involve all types of tangible objects, although usually more often are identified with monetary loans. Like other debt instruments, a loan requires a redistribution of financial assets over time between the borrower (indebted) and the debtor (the creditor).

The borrower initially receives an amount of money from the lender to be paid back, often in the form of periodic installments, to the lender. This service is usually provided with certain costs which are referred to as interest on the debt. Borrowers can also get restrictions in the form of loan conditions.

Before applying for a loan you should know how to calculate the percent interest on a loan to check the correctness of the interest calculation specified on your credit.

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Details

Grade: High School

Subject: Mathematics

Keyword: loan, payment, borrowers

Answer:

The correct answer is A. 45.2

Step-by-step explanation:

1. Let's review all the information provided for solving this question:

Number of trees of the sample = 31

Number of trees of the sample with a height between 60 and 65 feet tall height = 3

Number of trees of the sample with a height between 65 and 70 feet tall height = 3

Number of trees of the sample with a height between 70 and 75 feet tall height = 8

Number of trees of the sample with a height between 75 and 80 feet tall height = 10

Number of trees of the sample with a height between 80 and 85 feet tall height = 5

Number of trees of the sample with a height between 85 and 90 feet tall height = 2

2. Let's calculate the percentage of the trees that are less than 75 feet tall:

Percentage of the trees less than 75 feet tall = [(Number of trees of the sample with a height between 60 and 65 feet tall + Number of trees of the sample with a height between 65 and 70 feet tall + Number of trees of the sample with a height between 70 and 75 feet tall)/Number of the trees of the sample] * 100

Replacing with the real values, we have:

Percentage of the trees less than 75 feet tall = [(3 + 3 + 8)/31] * 100

Percentage of the trees less than 75 feet tall = [(14)/31] * 100

Percentage of the trees less than 75 feet tall = 0.451613 * 100

Percentage of the trees less than 75 feet tall = 45.1613% = 45.2% (Rounding to one decimal place)

The correct answer is A. 45.2