An angle measures 82° less than the measure of its complementary angle. What is the measure of each angle?

Answer:

Jenny owes her sister 9.3 dollars.

Step-by-step explanation:

23.63 - 16.33 = 9.3

Answer:

4x²+2x-30

Step-by-step explanation:

(x+3) 2(2x-5)

(x+3) (4x-10)

4x²-10x+12x-30

4x²+2x-30

The probability that the father and son will obtain a kill if they both fired at an animal the same time is 0.9

The probability of an event is the likelihood of the occurrence of event.

The average number of animals the father kills every 5 shots he takes = 2

The average number of animals the son kills every 2 shots he takes = 1

[tex]Probability = \dfrac{Number \ of \ required \ items}{Number \ of \ possible \ outcomes}[/tex]

Which gives:

The probability that the father kills an animal = [tex]P(F) = \dfrac{2}{5} = 0.4[/tex]

The probability that the son kills an animal is; [tex]P(s) = \dfrac{1}{2} =0.5[/tex]

The probability that if the father and the son fires at the same animal, the probability that they will obtain a kill, which is the probability that the animal is killed , P(A) = The probability that the father kills the animal + The probability that the son kills the animal

Which gives: P(A) = 0.4 + 0.5 = 0.9

The probability that the animal will be killed is approximately 0.9

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Given that of the new books the new books the new liberian ordered;

-1/3 are science

-2/5 are biography

Let s, b and f represent the fraction of science, biography and fiction of the new book.

substituting the values of s and b given;

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-5}x-14\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {-5\implies \stackrel{slope}{\cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5}\implies \cfrac{1}{5}}}[/tex]

so we're really looking for the equation of a line whose slope is 1/5 and it passes through (10, -4)

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \implies {\large \begin{array}{llll} y +4= \cfrac{1}{5} (x -10) \end{array}}[/tex]

25 new teachers joined the school such that the new ratio is 1 : 20 .

In mathematics, a ratio illustrates how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.

The total number of students is 2000

The ratio of teachers to students  is 3:80 .

Therefore the number of teachers = 3 × 2000 ÷ 80 = 75

Let x teachers joined the school.

Therefore new ratio = (x+75) : 2000

but the new ratio is 1 : 20

Therefore 1 : 20 = (x+75) : 2000

Simplifying we get:

x + 75 = 100

or, x = 25

Therefore the number of teachers who joined the school is 25 .

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The probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams is 0.4339.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 3316 grams - 54 grams = 3262

μ = mean = 3316 grams

σ = standard deviation = 324 grams

z-score = (3262 - 3316) / 324

z-score = -54 / 324

z-score = -0.1667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -0.1667

Using interpolation of values,

probability = 0.4339

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Answer:

x = 12

Step-by-step explanation:

3/4x = 9

x = 9/1(4/3)

x = 12

Answer:

Step-by-step explanation:

y=652/4

convert decimal to a fraction

46/125=5

multiplying by both sides of the equation by 125/4

y=652/4 = 156 1/4

The temperature in salt lake city will be 0° Celsius.

Temperature tells us about the degree of hotness or coldness of a body. According to the thermodynamics, temperature is a measure of the average kinetic energy of the atoms or molecules in the system.

Given is Salt Lake City where it is 8˚ colder than it is in Houston.

The degree of coldness on Celsius scale increase as the temperature tends to negative values and degree of hotness on Celsius scale increase as the temperature tends to positive values. The temperature in Houston is 8° Celsius. Since, the temperature is 8 degrees colder, we will subtract 8° from the temperature value in Houston. Therefore, temperature in salt lake city will be -

T[S] = + 8 - 8 = 0° Celsius

Therefore,  the temperature in salt lake city will be 0° Celsius.

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Answer:

7A, 8D

Step-by-step explanation:

The compound interest formula is as followed

[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]

A = accumulated amount

P = principle

r = interest rate

n = compounding

t = time

The accumulated amount is represented by f(x).

The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000

The interest rate is 5%. This needs to be converted into a decimal.

5% = 0.05 = r

The money is compounded annually, thus n = 1.

The time is represented by x. x = t.

thus

[tex]f(x) = 2000(1+0.05)^{x}[/tex]

After six years, you simply find f(6), or substitute 6 into x.

f(6) = 2000(1.05)^6 = $2,680.19

Answer: x < -6

Step-by-step explanation:

1) Bring 1 to the other side

x/-2 > 3

2) Bring -2 to the other side. The sign flips when the number multiplied or divided is negative

x < -6

The solution to the equation is x = 5.24

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

(x - 3)^2 = 5

Take the square root of both sides

So, we have

x - 3 = 2.24

Add 3 to all sides of the equation

So, we have

x = 5.24

Hence, the solution is x = 5.24

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Answer: ask your teacher

Step-by-step explanation:u have to multiply

Answer:

d=12

Step-by-step explanation:

8d+4+6d+8 = 180 (Straight angle = 180)

14d+12=180

14d=168

d=12

:]

Answer:

D =12

Step-by-step explanation:

8d+4+6d+8 =180 (being a linear pair)

14d+12=180

14d=180-12

14d=168

d= 168/14

d=12#

The value of the absolute value expression given; | 1.1n | for n > 1 as required in the task content can be classified as; Choice B; >1.

It follows from the task content that the best classification of the expression | 1.1n | for n > 1 be determined.

Since the domain of variable n is such that n > 1, it follows that 1.1 × n > 1.1.

There, it follows that; 1.1n > 1.1 > 1.

By definition; The absolute value |n| of any real number n is the non-negative value of x irrespective of its sign. For instance, the absolute value of 15 is 15, and also the absolute value of −15 is also 5.

Hence, the absolute value sign; | 1.1n | indicates positive values.

Ultimately, the correct classification of.the expression is; Choice B; > 1.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (1500)(0.07)(8) \implies I = 840[/tex]

The probability of a head and an even number is 1/4.

Probability is the occurrence of a certain event out of the total events than can occur in a given context.

Given event is a coin is tossed and then a die is rolled.

∴ The sample space (S) is = (H,1), (T,1), (H,2), (T,2), (H,3),(T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6).

So, the number of sample spaces N(S) = 12.

The number of heads and an even number N(H,E) = 3.

∴ The probability of a head and an even number is = N(H,E)/N(S).

= 3/12.

= 1/4.

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Answer:

2:20 pm to 5:57 pm is 3 hours and 37 minutes.

Answer:

3 hours and 37 minutes.

Step-by-step explanation:

5:57

-2:20

= 3:37

Given,

Total distance [tex]=2\frac{1}{2}[/tex] miles

You run 1/3 of that distance on a hill.

Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles

You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles

Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles

Answer:

[tex]23+4x(2+5)<15-5x(8-7)]2^5[/tex]

Given

Major axis of length = 12

Foci at ( 9 ,1 ) and ( -1, 1 )

Find

Equation of an ellipse

Explanation

As we know , major axis = 2a = 12

thus a = 6

the midpoint between the foci is the center , so

the distance between the foci is equal to 2c

now,

so , the equation of an ellipse is

Final Answer

The equation of an ellipse

1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:

2) Based on that, we can do the following to find the next two terms:

Thus, the next terms are -5 and 2

The correct answer is 0.4834

There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.

The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14

The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.

The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.

p = 0.14

q = 1 - p = 1 - 0.14 = 0.86

n = 12

x = 2

We need to find: P( x < 2)

Fewer than 2 tornadoes means either 1 or 0 tornado. So,

P(x < 2) = P(x=0) + P(x=1)

the likelihood of less than two tornadoes occurring in a 12-year period is 0.4834

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Answer:

see explanation

Step-by-step explanation:

(a)

common ratio r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{14}{28}[/tex] = [tex]\frac{1}{2}[/tex] = 0.5

(b)

to find the next term, multiply the previous term by r = 0.5

14 × 0.5 = 7

7 × 0.5 = 3.5

3.5 × 0.5 = 1.75

the next 3 terms in the sequence are 7 , 3.5 , 1.75

⇒In a geometric sequence to find the common ratio(r) we use the formula

[tex]r=\frac{T_{2} }{T_{1} }[/tex]

But in general we use the formula is [tex]r=\frac{T_{n+1} }{T_{n} }[/tex]

In this case we are going to use

[tex]r=\frac{14}{28} \\r=\frac{1}{2}[/tex]

⇒The common ratio of the sequence is [tex]\frac{1}{2}[/tex], to get the 3 consecutive terms you are going to multiply the current term by the common ratio which in this case is [tex]\frac{1}{2}[/tex]

[tex]T_{3} =T_{2} * r\\\\T_{3}=14(\frac{1}{2} )\\T_{3} =7[/tex]

[tex]T_{4} =T_{3} *r\\T_{4}=7(\frac{1}{2} )\\T_{4}=\frac{7}{2}[/tex]

[tex]T_{5}=T_{4} *r\\T_{5}=\frac{7}{2} *\frac{1}{2} \\T_{5}=\frac{7}{4}[/tex]

If you have any questions ask me as soon as possible.

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Hello!

To evaluate h(3)

 ==> must plug '3' into x's position in the equation:

    [tex]h(3)=3^2-4(3)+5\\h(3)=9-12+5=2[/tex]

Hope that helps!

Answer:

2

Step-by-step explanation:

substitute 3 for the x

3²-4(3)+5

9-12+5

2