A total of $5000 is invested: part at 7 % and the remainder at 15 %. How much is invested at each rate if
the annual interest is $480?

Answer:

Men Women Total

Exercise less than 7 hours per week

Men:108

Women:81

Exercise 7 or more hours per week

Men:84

Women:27

Step-by-step explanation:

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

and to get it, we only need two points off a line, hmmm let's use those two points in the picture below.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{6}{4}\implies \cfrac{3}{2}[/tex]

Answer:

Area (A)  0.0682

Step-by-step explanation:

The sketch for the region enclosed by the given curves can be found in the image attached below.

From the image below;

The two curves intersect in the area of tan 9x = 2 sin 9x

Recall that:

making x the subject; then:

The subdivision of the domain is in two intervals

where;

Area (A) =

Area (A) = 0.06818

Area (A)  0.0682

Answer:

[tex]y = -\frac{1}{3}x + 5[/tex]

Step-by-step explanation:

To being, slope intercept form is the infamous y = mx + b form. In which, m is equal to the slope and b is equal to the y-intercept. (1) To solve this, begin by finding two points of the line. One easy point to find is when x = 0 as it intersects with the y-axis. Two points are: (0,5) and (-3,6). (2) Next, use the slope formula to solve for the slope. The slope formula is [tex]\frac{y2-y1}{x2-x1}[/tex]. Plug in the y and x values;  [tex]\frac{6-5}{-3-0}[/tex]. Simpliify the fraction; [tex]\frac{1}{-3}[/tex] --> [tex]-\frac{1}{3}[/tex]. Therefore -1/3 is our slope. (3) To solve for b, the y-intercept, set up the slope-intercept equation with the newfound slope (y = -1/3x + b) and plug in a point for the y and x values. Doing this will isolate the b so you can solve for it.

6 = -1/3(-3) + b

6 = 1 + b

-1    -1

5 = b

Therefore the y-intercept (b) is 5. (4) The final step is to combine the information into the slope-intercept form; y = -1/3x + 5. Good luck!

Answer:

z score = .2843

Step-by-step explanation:

25 is 2 below 27

   this is  2/3.5 = .5714  S.D. below mean

      z-score  . 2843

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

so let's start ~

General term , [tex] A_{n} [/tex] = 3n + 10

let's consider certain values of n to get some information with us which will help us solve the problem further !

let's first consider , n = 1 ! then ,

[tex]3n + 10 = 3(1) + 10 \\ \dashrightarrow \: 13[/tex]

now , let's consider n = 2

[tex]3n + 10 = 3(2) + 10 = 6 + 10 \\ \dashrightarrow \: 16[/tex]

then , let's consider n = 3

[tex]3n + 10 = 3(3) + 10 = 9 + 10 \\ \dashrightarrow \: 19[/tex]

hence ,

now we've with us an AP which is as follows -

[tex]13 \: , \: 16 \: , \: 19 \: ......[/tex]

from this Arithmetic Progression ,

we can know that

a = first term = 13

d = common difference = 16 - 13 = 19 - 16 = 3

now ,

[tex]A _{n} = a + (n - 1)d \\ \implies \: A _{150} = 13 + (149)(3) \\ \implies \: A _{150} = 13 + 447 \\ \pink{\implies \: A _{150} = 460}[/tex]

hope helpful :D

Answer: No, the events are not mutually exclusive

Work Shown:

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = 0.51 + 0.79 - 0.66

P(A and B) = 0.64

Since the result is not zero, this means the events are not mutually exclusive.

Mutually exclusive events are ones that cannot happen at the same time. Example: getting a "2" and a "3" on the same roll of a number cube.

Answer:

Its D I did my math

Step-by-step explanation:

Answer:

D. I worked the math out.

Any equation that starts with y =7x

Parallel lines have the same gradient.

(No options to choose from)

Hope this helps!

Any Equation start with y = 7x + c is parallel to given equation.

To determine whether or not two lines are parallel, the formula for parallel lines is used. When we have the slopes of two lines that we want to compare, we can use the parallel line formula. The parallel lines' distances never change.

Given Equation

y = 7x + 5

and line k

line k is parallel  to equation y = 7x + 5

for parallel lines

The formula for determining whether two lines are parallel is as follows for any two lines with the equations y = m₁ x + c₁ and y = m₂x + c₂:

where m₁ and m₂ are the slopes of the two lines. m₁ = m₂.

given equation y = 7x + 5,

here m₁ = 7 and c₁ = 5

the line which is parallel to equation should be

y = 7x + c

where m₂ = m₁ = 7 and c₂ = c

Hence equation y = 7x +c is parallel to given equation.

Learn more about Parallel lines;

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Answer:

i think. 8 times 12 = 96 times 20 = 1,920

Answer:

39.5 in^3

Step-by-step explanation:

lol someone had the same question

The formula for a cone is (pi)(r^2)(h/3)

Since we have to use 3.14 for pi, we plug 3.14 in for pi:

(3.14)(r^2)(h/3)

The radius is 2 and the height is 8, so we plug in those numbers:

(3.14)(2^2)(8/3)

Simplify:

(3.14)(4)(2.666...)

Multiply:

(12.56)(2.666...) -> 39.49333...

Finally, we round 39.49333... to the tenths place:

39.5

Hope this helps :)

Answer:

23 Cm(2)

Step-by-step explanation:

Sincerest Apologies if it is incorrect

if it's not 23 it may be:

26 Cm(2)

Answer:

use the quadratic formula

Step-by-step explanation:

from the equation a=6 b=-14 c=-9

from the quadratic formula

[tex]x = ( - b {+ or - } \sqrt{ {b}^{2} + 4ac} ) \div 2a[/tex]

therefore insert in the values of a, b and c

[tex]x = ( - ( - 14) + or - \sqrt{ {( - 14)}^{2} + 4 \times 6 \times ( - 9)} ) \div 2 \times 6[/tex]

x=2.858148594

X=-0.52481526

after inserting

Answer:

  96.76 cm²

Step-by-step explanation:

The area of a rectangle is the product of its length and width.

__

  A = LW

  A = (11.8 cm)(8.2 cm) = 96.76 cm²

Answer:

96.76 cm2

Step-by-step explanation:

Answer:

4/x-8=8/2

4/x-8=4

4=4(x-8)

4=4x-32

4+32=4x

36=4x

dividing through by 4

x=9

converting to the nearest tenth will be 9.0

therefore x=9.0

Answer:

Total amount of tickets is 48

Step-by-step explanation:

Step 1:  Determine the amount of tickets they solid in all

We see that the movie theater has a ratio of 4 adult tickets for every children ticket which means that wen a child purchases a ticket there are 2 adult tickets that come along.

32 adult tickets / (2 adult tickets per child)

16 children tickets

Total tickets: 32 adult tickets + 16 children tickets = 48 tickets

Answer:  Total amount of tickets is 48

The number of people who voted for Cat-urday Night Fever as the best comedy film is given by the equation A = 182 people

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of people who voted for the comedy film be = A

Now , the equation will be

The total number of people = 280 people

The percentage of people who voted for the best comedy film = 65 %

So , number of people who voted for the comedy film A = percentage of people who voted for the best comedy film x total number of people

Substituting the values in the equation , we get

Number of people who voted for the comedy film A = ( 65 / 100 ) x 280

On simplifying the equation , we get

Number of people who voted for the comedy film A = 0.65 x 280

Number of people who voted for the comedy film A = 182 people

Therefore , the value of A is 182 people

Hence , the number of people is 182 people

To learn more about equations click :

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Answer:

0.43

Step-by-step explanation:

Just take out the % sign and divide it by 100.

For your example:

43%

Take out the percentage

43

Divide it by 100.

0.43

And there is your answer :)

Answer:

You should move the decimal 2 place

Step-by-step explanation:

43/100 = 0.43

Answer:

43º

Step-by-step explanation:

Angles in a straight line = 180º so:

180 - (90+47) = 43º.

Alternate angles are equal so the x is also 43º.

Answer:

135

Step-by-step explanation:

[tex]d = 45t[/tex]

[tex]d(3) = 45( 3) = 45 \times 3 = 135[/tex]

[tex]d(3) = 135[/tex]

I HOPE IT HELPED YOU

Answer:

135

Step-by-step explanation:

sub 3 in place of t then times and it 135

Answer:

• No

• Yes

• Yes

• No

Step-by-step explanation:

To determine if the 4 given values of y are solutions to the inequality, start by solving the inequality. Solving an inequality is just like that of an equation, except that the direction of the sign changes when the inequality is divided by a negative number.

-2y +7≤ -5

Subtract 7 on both sides:

-2y≤ -5 -7

-2y≤ -12

Divide by -2 on both sides:

y≥ 6

This means that the solution can be 6 or greater than 6.

-10 and 3 are smaller than 6 and are not a solutions, while 7 and 6 satisfies the inequality and are therefore solutions.

_______

Alternatively, we can also substitute each value of y into the inequality and check if the value is less than or equal to -5.

Here's an example to check if -10 is a solution.

-2y +7≤ -5

When y= -10,

-2y +7

= -2(-10) +7

= 20 +7

= 27

Since 27 is greater than 5, it is not a solution to the inequality.

Answer:

A=(3.14)r²

Step-by-step explanation:

First you find your radius if it is a diameter you divide it by 2

Second you multiply the radius by pi (π=3.14)

lastly you square your answer

hope this helps!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

[tex] \textbf{Since it's a right angled Triangle we can } \\ \textbf{ use Pythagoras theorem } [/tex]

[ [tex] \textsf{Cos(29°)= 0.875} [/tex] ]

[tex] \textsf{I hope you understood the procedure} [/tex]

Answer:    [tex]-\frac{240}{289}[/tex]

=========================================================

Explanation:

Use the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex] and plug in the fact that [tex]\cos(\theta) = \frac{8}{17}\\\\[/tex]

Isolating sine leads to [tex]\sin(\theta) = -\frac{15}{17}\\\\[/tex]. I'm skipping the steps here, but let me know if you need to see them.

The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.

Therefore,

[tex]\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\[/tex]

Answer:

10√2

Step-by-step explanation:

We can form a triangle with the clues in the question, and use the formula A²+B²=C²

Now, we plug in our values.

5²+B²=15²

25+B²=225

B²=200

B=√200

√200 =√2x2x2x5x5 = 10√2

Answer:

D) It is 1:5.

Step-by-step explanation:

[tex] \frac{4}{20} = \frac{1}{5} [/tex]

Answer:

12

Step-by-step explanation:

Jim's currect age is x.

In 16 years, JIm will be x + 16.

In 4 years, Jim will be x + 4.

x + 16 = 3x

-2x = -16

x = 8

x + 4 = 8 + 4 = 12

Answer:

True, True, True, False

Step-by-step explanation:

Step-by-step explanation:

-1/7 = -3/2x

1/7 = 3/2x

x = 1/7×2/3

= 2/21 :")