What number multiplied by 7/9 as a product of one

Answer:

(a)  [tex]\frac{620}{3195}[/tex]

(b) [tex]\frac{645}{3195}[/tex]

Step-by-step explanation:

Relative frequency of an event = Event Frequency/Total Frequency

In this case the event is the number of responses for each reason and the total frequency is the sum of all responses.

Total Responses = 583 + 620 + 187 + 163 + 558 + 645 + 439 = 3195

(a) What is the relative frequency for the reason "study hard"?
= Number of responses for "study hard" / 3195

= 620/3195

==> [tex]\frac{620}{3195}[/tex]   Answer to (a)

(b) What is the relative frequency for the reason "have a goal in mind"?

= Number of responses for the reason "have a goal in mind"/3195

= 645/3195

==> [tex]\frac{645}{3195}[/tex]   Answer to (b)

I think it is OK to leave it as it is without reducing the fraction any further

Answer:680

Step-by-step explanation:

160x.75=120

160x1.5=240

160x2=320

Betsy needs to  invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.

Interest is calculated by multiplying the rate with the principal.

Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.

We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000

Now we can write the necessary equation to solve for x.

or, 0.13x+0.03(60000-x) = 5000

or, 0.13x+1800-0.03x = 5000

or, 0.1x+1800 = 5000

or, 0.1x = 3200

or, x = 32000

So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.

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The amount will be $141647.55.

we need to use the present value of an annuity formula:

the formula used to determine the present value factor of an annuity is:

present value annuity factor = [1 - 1/(1 + i)ⁿ ] / i

we must divide this into 2 parts:

the first part will deal with the $19,00 monthly payment

the second part deals with the $38,000 monthly payment

i = 9.75% / 12 = 0.8125%

n (first part) = 36

n (second part) = 24

the PV annuity factor for first part = [1 - 1/(1 + 0.8125%)³⁶ ] / 0.8125% = 31.1043

the PV annuity factor for second part = [1 - 1/(1 + 0.8125%)²⁴ ] / 0.8125% = 21.7251

loan = ($219,00 x 31.1043) + ($38,00 x 21.7251)//(1 + 0.8125%)³⁶ = $59092.17 + $82555.38 = $141647.55

hence we get the amount as $141647.55

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The missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is -33/4.

Let the missing ccordinate of the ordered pair be m.

According to the given question.

We have an equation 6x - 4y = 9.

Here, we have given a ordered pair (-4, ?) which satisfy the given equation 6x - 4y = 9.

Therefore, the missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is given by

6x - 4y = 9

⇒ 6(-4) - 4(m) = 9

⇒ -24 - 4m = 9

⇒ -4m = 9 + 24

⇒ -4m = 33

⇒ m = -33/4

Hence, the missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is -33/4.

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Answer: Table  which had a constant of proportionality between y and x of 1/6

is table C

Step-by-step explanation:

The meaning of constant proportionality is very simple and that is

ratio of y and x

here

y/x=1/6;

therefore we have to check various options

checking option C

first part:

3/18=1/6;

second part:

(9/2)/27=1/6;(convert mixed fraction into improper fraction)

third part:

(11/2)/33=1/6;

hence ;

Table  which had a constant of proportionality between y and x of 1/6

is table C

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The value of x from the inequality is x < 3

An inequality is defined as a statement of an order relationship between two numbers or algebraic expressions.

Given the inequality;

3x + 1 < 10

To determine the solution, we take the followings steps;

collect like terms

3x < 10 - 1

Find the difference between the terms

3x < 9

Make 'x' the subject of formula

x < 9/ 3

x < 3

Thus, the value of x from the inequality is x < 3

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The number of weeks that it takes to empty the lake is; 350/11 weeks

We are told that Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

Let w = number of weeks required to empty the lake

let the completed job = 1 (an empty lake)

Thus;

w/14 - w/25 = 1

Multiply through by 350 to get;

25w - 14w = 350

11w = 350

w = 350/11 weeks

Thus, the number of weeks that it takes to empty the lake is; 350/11 weeks

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Answer:

USE air math

Step-by-step explanation:

hope that helps

Answer:

(5x) + 3 = 7

Step-by-step explanation:

Times means 'The answer when you multiply' So we are working in multiplication. ( x )

5x is the multiplication.

It says 'and' which can also mean addition. So we add 3. So far our equation is: (5x) + 3 (Brackets are needed as we are multiplying 5 by x and not multiplying 5 by x+3)

Lastly it says the answer must be 7 so we add that at the end. So the answer is:

(5x) + 3 = 7

From the steps below, it has been proved that  by transitive property of congruence, we can say that; ∠CON ≅ ∠BOM

We are given;

∠AOM ≅ ∠DON

To prove that;

∠CON ≅ ∠BOM

Now, from the image attached, we can say that;

∠BOM ≅ ∠DON because of vertical angles theorem

Similarly, we can say that ∠AOM ≅ ∠BOM due to transitive property of congruence.

Also, we can say that from vertical angles theorem, ∠AOM ≅ ∠CON

Finally, since  ∠AOM ≅ ∠BOM, then by transitive property of congruence, we can say that;∠CON ≅ ∠BOM

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Answer:

17.75

Step-by-step explanation:

253.63 ×0.07=17.7541

In order to answer this issue, I need to identify an LCD, or least common denominator—something that unites all of the group members. We had all previously worked for the same employer, so that was our common denominator.

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.

Prime number seven.

7*8 = 56

56 is the lowest common factor.

3/7 * 8/8 = 24/56

5/8*7/7 = 35/56

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Answer: 10

Step-by-step explanation: First you decide that each container can fill 3/4 of a cup. You have 8 cups so you need to divide 8 by 3/4 which will give you the answer of 10.666 repeating so the answer is you can only fill up 10 containers.

Answer:

4x + 27

Step-by-step explanation:

12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)

12x + 27 - 8x Combine like terms (12x, -8x)

The linear speed in miles per hour of the tip of a lawnmower blade spinning is 0.0601509076 miles per hour and angular velocity is 293.276 rad/hr.

The measurement of a moving object's actual distance traveled is called linear speed. Linear speed is the rate of motion of an item along a straight line. It is the distance traveled along a linear path in the allotted amount of time.

2800 rotations per minute on a lawnmower blade.

Specifically, the frequency of the blade is 2800 revolutions per hour,

f = 2800 / 60, or 46.66.

The angular velocity is

ω = 2πf

where f = frequency

ω = 2 × 3.14 × 46.7

ω = 293.276 rad/hr

The diameter of the circle centered at the blade's middle determines the path's breadth.

26 inches in diameter

radius = 26 / 2 = 13

13 inch = 0.0002051 miles

Velocity is given by -

V = ωR

V = 293.276 × 0.0002051

Velocity = 0.0601509076 miles per hour

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The value of x in given diagram is x=3;

The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.

Area of triangle SXY = 1/2 × SX × (x-2);

Area of triangle STR = 1/2 × ST × (x+3);

Area of trapezium XTRY = 1/2 × (x+3+x-2) × XT;

Area of triangle SXY = Area of triangle STR - Area of trapezium XTRY;

SX × (x-2) = ST × (x+3) - (2x + 1) × XT;

As; SX = TX = ST/2;

(x-2)/2 = (x+3) - (2x+1)/2;

x - 2 = 2x + 6 -2x -1

x = 3;

A triangle is a closed figure that has three vertices, three sides, and three angles.  It is one of the most fundamental geometric forms, and it is represented by the symbol△. Triangles in mathematics can be categorized according to their sides and angles into many categories.

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The expression  can be simplified to:

x + y/100

Where x is the month and y the day. This is why it always works.

Let's define the two variables x and y as the month of your birth and the day of your birth respectively.

Now let's write the expression by following the steps, you should get:

((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100

Now let's simplify the expression we will get:

((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100

(((91x - 13 + y + 3)*11 - x - y)/10 + 11)/100

(((91x - 10 + y)*11 - x - y)/10 + 11)/100

((1001x - 110 + 11y - x - y)/10 + 11)/100

(( 1000x - 110 + 10y)/10 + 11)/100

You already can see what will happen here:

(( 1000x - 110 + 10y)/10 + 11)/100

(100x - 11 + y + 11)/100

(100x + y)/100 = x + y/100

So the expression will do the exact same thing for every values of x and y that you decide to use, it does not depend on your exact date of birthday.

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Answer:

[tex]\dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{4+\sqrt{3}}{3+\sqrt{-3}}[/tex]

[tex]\textsf{Apply radical rule}:\quad \sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}\sqrt{-1}}[/tex]

[tex]\textsf{Apply imaginary number rule}:\quad \sqrt{-1}=i[/tex]

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i}[/tex]

Multiply by the conjugate of the denominator:

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i} \cdot \dfrac{3-\sqrt{3}i}{3-\sqrt{3}i}[/tex]

[tex]\implies \dfrac{(4+\sqrt{3})(3-\sqrt{3}i)}{(3+\sqrt{3}i)(3-\sqrt{3}i)}[/tex]

[tex]\implies \dfrac{12-4\sqrt{3}i+3\sqrt{3}-\sqrt{3}i\sqrt{3}}{9-3\sqrt{3}i+3\sqrt{3}i-\sqrt{3}i\sqrt{3}i}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-4\sqrt{3}i-3i}{9-3i^2}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3i^2}[/tex]

[tex]\textsf{Apply imaginary number rule}:\quad i^2=-1[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3(-1)}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{12}[/tex]

Separate the fractions:

[tex]\implies \dfrac{12+3\sqrt{3}}{12}-\dfrac{(3+4\sqrt{3})i}{12}[/tex]

Simplify:

[tex]\implies \dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]

50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Market research was undertaken to determine whether an ad campaign was successful for the software company.

Total number of people = 15 + 75 = 90

The number of people who said yes = (2/5)90 = 36

The number of people who said no = 90 - 36 = 54

The number of men said yes = (6/15)x15 = 6

The number of men said No = 15 - 6 = 9

The number of women who said no = 54 - 9 = 45

Percentage = (45/90)x100

The percentage of women who said ‘no’ out of the total survey population:

= 50%

Thus, 50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.

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The actual problem will be  9000 % 700, with the remainder 600 and quotient 12.

Since we are with the actual problem, which is 8,950 % 695, here the dividend is 8950  and the divisor is 695, the actual division we come up with the 12 as quotient and remainder 620. Now making the expression simple  using the round-off rule, here  in  the dividend  8950, the last two digits are 50, so we can round off it to 9000 and in the  divisor  695,  the last digit is 5, so we add 1 in the preceding  number converting it to 700, after the actual division of the estimated expression, the quotient we come up with is 12, and the remainder is 600.

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Answer:

The length should equal 27.

The width should equal 13.

A: P= 2L+ 2W

B: L=2W+1

Step-by-step explanation:

Perimeter is always equal to all of the sides added up.

You can find out the width and length by subsititution.

80=2(2W+1) +2W

80=4W+2+2W

80=6W+2

78=6W

W=13

L=(13*2)+1

L=27

Answer:

72

Step-by-step explanation:

I am pretty certain that the answer is 72.

Steps:

[tex]\frac{8}{36}[/tex] [tex]\frac{x}{9}[/tex]

Cross-Multiply and Divide.

8*9 = 72

72 / 36 = 2

2/9 = 0.222222

8/36 = 0.222222

2/9 = 0.2222222

Answer:

i think 114ft

Step-by-step explanation:

Answer:

114 FT

Step-by-step explanation:

Perimeter formula: P = 2 (l + w)
P = 2 (40 + 17)
Use distributive property or PEMDAS

Distributive property: P = 80 + 34
P = 114

PEMDAS: P = 2(57)
P = 114

You get 114 either way

Winter would last for 14,600 days

Planet can be described as celestial bodies that move around the sun. The earth and Neptune are typical examples of planets. There are 8 planets in the solar system.

Other planets have different seasons same way as Earth

Neptune's season last for 40 years

Therefore the number of days that winter would last can be calculated by multiplying the number of years which is 40 by the number of days in a year which is 365

1 year is 365 days

Since it 40 years then we multiply by 365

= 365 × 40

= 14,600

Hence Winter would last for 14,600 days

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The number 67 and 113 are not the multiples of 3,6 and 7.

Multiples are the results of multiplying one whole number from another whole number.

Now, for the given question;

As, 67 and 113 are not completely divisible by 3. They are not multiple of 3.

67 and 113 are not entirely divisible by 6. So, they are also not the multiple of 6.

Now, 67 and 113 are also not entirely divisible by 7. Thus, they are also not the multiple of 7.

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Answer: 78

Step-by-step explanation:

first, you multiply 8 by 9 then you get 72, and then you can add the leftover cherries with 72 so 72 + 6 = 78

Answer:

Step-by-step explanation:

78