Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?
First account:
Second account:

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A T-score of -3.6 indicates that the individual has a severe case of osteoporosis

A T-score is a standard score used to compare an individual's bone mineral density (BMD) to that of a healthy young adult population. A T-score of -3.6 on a BMD test indicates that the individual's BMD is significantly lower than that of a healthy young adult. Specifically, it means that the individual's BMD is 3.6 standard deviations below the average BMD of a healthy young adult.

A T-score of -2.5 or lower is considered to indicate osteoporosis, which is a condition characterized by low bone density and an increased risk of fractures. Therefore, a T-score of -3.6 indicates that the individual has a severe case of osteoporosis, and the doctor will likely recommend treatment such as medication and lifestyle changes to help increase bone density and reduce the risk of fractures.

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Answer:

x (number of games) = 8

Step-by-step explanation:

We want these two to be equal, which means we want:

4.50x + 5 = 4.75x + 3

We will minus 4.50x and 3 from both sides, giving us:

2 = .25x

Then, multiply by 4 to get a whole number of x, which gives us:

x = 8

Now, we will check our answer. We have:

4.50 * 8 + 5 = 4.75 * 8 + 3

36 + 5 = 38 + 3

41 = 41

So this proves x = 8.

So, the amount of games where the price would be the same is 8, x = 8.

Hope this helped!

Step-by-step explanation:

now you should be able to dive these things yourself.

A no

(1/4)v = 4

4×(1/4)v = 4×4

v = 16

this is not v = 4

B no

n + 4 = 25

n + 4 - 4 = 25 - 4

n = 21

this is not n = 17

C yes

2z = 28

2z/2 = 28/2

z = 14

Answer:

Circumcenter (x) = 2

Circumcenter (y) = -2

Answer:

(2, -2)

Step-by-step explanation:

Midpoint of BC: ([-4 + 8]/2, (4 + 4)/2) = (2, 4)

Perpendicular bisector of BC has equation: x = 2

Midpoint of AC: ([8 + 8]/2, (-8 + 4)/2) = (8, -2)

Perpendicular bisector of AC has equation y = -2

Point of intersection of the two perpendicular bisectors:

(2, -2)

Answer: (2, -2)

13 number of runners run at most 2 miles per day .

calculation is explained below as

at 2 miles = 6 runners run

at 3 miles = 4 runners run

at 4 miles = 2 runners run

at 5 miles = 1runners run

on adding to calculate how many number of members run at most 2 miles per day is    = 6 + 4 + 2 + 1 = 13 .

hence 13  number of members run at most 2 miles per day .

A number line plot is a simple way of  visual representation of data patterns at the coordinate axis. on comparing the height of the specific columns,  the least frequently of occurring number can be calculated. The number line of plot becomes a bar graph when the  box is drawn around the Xs or dots in each and every column. A horizontal line, also called  as  x-axis, with equal intervals which are labelled with values which makes  a number line plot. Xs or dots can be used to describe or evaluate  the frequency in which a number, or a set a defined numbers, occurs on number line . Stacks of such producing  Xs or dots that are used to represent data on the axis is known as plot number. .

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Answer:

Step-by-step explanation:

Plan C is the least expensive plan, as it has the lowest subtotal of $48.00 plus 6.5% fees and taxes.

The equation that represent the relationship between pounds of garbage y and of days x is y = 4.5x

Direct variation describes a simple relationship between two variables . We say y varies directly with x , then y=kx. for some constant k , called the constant of variation or constant of proportionality .

From the graph when y = 4.5 , x = 1 and when y = 9 , x = 2. we can take any of these values to find K

y = kx

9 = 2k

therefore K = 9/2 = 4.5

representing K for 4.5 in y = kx

then, y = 4.5x

therefore the equation of the relationship between y and x is y = 4.5x

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Answer: The answer is 0.25 inches every minute

Step-by-step explanation: The equation tells you that the pool started at 30 inches (0.25t+30). It says that the pool's depth rises 0.25 inches every minute. So the answer is that the pool started out as 30 inches (which is the y-intercept) and rose 0.25 inches every minute.

Hope this helped

Answer:

Step-by-step explanation:

By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

table shows the relation y = kx .

so the given x values = 2,3,5,8 .

and the y values = 5,7.5,12.5,20

From the relation y = kx .

By substituting the given values

we get,

y = kx

y=5 x = 2

5 = k * 2

k = 2.5

y=7.5 x = 3

7.5 = k*3

k = 7.5/3

k = 2.5

y = 12.5 x = 5

12.5 = 5*k

k= 12.5 / 5

k = 2.5

y=20 x = 8

20 = k*8

k = 20/8

k = 5/2

k = 2.5

Hence, By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x - 1 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line

to find c substitute (8, 4 ) into the partial equation

4 = [tex]\frac{3}{4}[/tex] (8) + c = 6 + c ( subtract 6 from both sides )

- 2 = c

y = [tex]\frac{3}{4}[/tex] x - 2 ← equation of parallel line

---------------------------------------------------------------

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , then

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (8, 4 ) into the partial equation

4 = - [tex]\frac{4}{3}[/tex] (8) + c = - [tex]\frac{32}{3}[/tex] + c ( add [tex]\frac{32}{3}[/tex] to both sides )

4 + [tex]\frac{32}{3}[/tex] = c , then

c = [tex]\frac{44}{3}[/tex]

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{44}{3}[/tex] ← equation of perpendicular line

[tex]\angle 3[/tex] and [tex]\angle 6[/tex]

The word "and" in probability implies that we use the Multiplication rule.

The correct option is Option D.

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

The relationship between two events is explained by the probability multiplication rule.

Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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The proof of the vertical angle theorem as required is explained in the answer below:

What are vertical angles?

Vertical angles are two angles that have the same properties and measure of their angles. Majorly these angles are opposite to each other and formed by the same extended lines.

So that, the required proof of the vertical angle theorem is;

             STATEMENT                                            REASON

1. AC intersect BD at E                                       Given

2. m<AEB m<DEA = 180^o                                 Linear pair theorem

3. m<DEC + m<DEA = m<AEB + m<DEA           Substitution property

4. m<DEC = 180^o - m<BEC                                Subtraction property

5. m<DEC = m<AEB                                             Vertical angle theorem

Therefore it can be deduced in the diagram that;

m<DEC = m<AEB           (vertical angle theorem)

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5-card hands have at least one club  2023203

5-card hands have at least two cards with the same rank 916,272

N[at least one club] = N[total ways] - N'[at least one club]

                               = N[total ways] - N[no clubs]

There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.

There are 2598960 possible hands, leaving us with 2598960-575757 ways.

Which is 2023203 hands.

How many 5 card hands will have (at least) two of the same number?

This is a standard deck. Take 2–10 to be what I mean by numbers.

N=∑k=24(91)(4k)⋅(125−k)(41)5−k+[(92)+(91)(41)](42)2⋅(111)(41)

+(91)(42)⋅(121)(43)+(91)(43)⋅(41)(42)

=(760,320+38,016+432)+114,048+2,592+864

=916,272

A standard deck of playing cards contains 13 unique ranks, each with 4 distinct suits. Since we are interested in only pairs from ranks 2 to 10, we shall define A be the collection of the 9 relevant ranks and B be the collection of the 4 ranks (ace, jack, queen, king) where pairs are not a consideration. Collection C is the union of A and B, which contains all 13 ranks.

When computing probabilities we need to select the ranks(s) from a collection and then choose a number of suits (cards). When ranks are chosen from either A or B they are also chosen from C. This is important since we might choose twice from the same collection. For example, we might choose a rank from A for a pair (9 choose 1) and later choose 3 ranks from C for singletons (12 choose 3).

To hopefully make understanding the logic easier, I have first chosen the ranks either from A, B, or C, and immediately following I have chosen the number of cards, which is always choosing from 4 suits. I have inserted a dot between different card selections.

We begin by computing the number of combinations with exactly 2, 3, and 4 of a kind from A. The singletons come from C.

N1=∑k=24(91)(4k)⋅(125−k)(41)5−k=760,320+38,016+432=798,768

We add the case of either two pairs from A or a pair from each of A and B. The singleton comes from C.

N2=[(92)+(91)(41)](42)2⋅(111)(41)=114,048

We add the case of a pair from A and 3 of a kind from C.

N3=(91)(42)⋅(121)(43)=2,592

Finally, we add the case of 3 of a kind from A and a pair from B. Note that the case of both 3 of a kind and a pair from A is the same as the case of both a pair and 3 of a kind from A, which has already been included.

N4=(91)(43)⋅(41)(42)=864

N=N1+N2+N3+N4=916,272

5-card hands have at least one club  2023203

5-card hands have at least two cards with the same rank 916,272

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The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.

Here we have given that the lens to form a well-focused image of the candle flame on the wall.

As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.

Here we have given the other is that same distance from the candle.

Then the position near the wall will yield a small image.

Here the position near the candle will produce a large image.

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Answer:

20° , 40° , 120°

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 6 = 9 parts

divide the sum of the angles in a Δ , 180° by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

2 parts = 2 × 20° = 40°

6 parts = 6 × 20° = 120°

the 3 angles are 20° , 40° and 120°

The vertex form of the parabolae equations are, respectively:

Parabolae are described by quadratic equations, whose standard and factor form are shown below:

Standard form

y = a · x² + b · x + c

Factor form

y = a · (x - r₁) · (x - r₂)

Where:

This equation can be modified into vertex form:

y - k = C · (x - h)²

Where:

The complete procedure to find vertex form is described below:

Now we proceed to find the vertex form of each expression:

Case 1

y = x² - 6 · x - 27

y = (x² - 6 · x + 9) - 36

y + 36 = (x - 3)²

Case 2

y = x² - 2 · x + 7

y = (x² - 2 · x + 4) + 3

y = (x - 2)² + 3

y - 3 = (x - 2)²

Case 3

y = x² + 10 · x

y + 25 = x² + 10 · x + 25

y + 25 = (x + 5)²

Case 4

y = x² + 14 · x + 50

y = (x² + 14 · x + 49) + 1

y = (x + 7)² + 1

y - 1 = (x + 7)²

Case 5

y = x² - 3 · x

y + 9 / 4 = x² - 3 · x + 9 / 4

y + 9 / 4 = (x - 3 / 2)²

Case 6

y = x² - 5 · x + 8

y = (x² - 5 · x + 25 / 4) + 7 / 4

y - 7 / 4 = (x - 5 / 2)²

Case 7

y = 2 · x² + 8 · x

y = 2 · (x² + 4 · x)

y + 2 · 4 = 2 · (x² + 4 · x + 4)

y + 8 = 2 · (x + 2)²

Case 8

y = 3 · x² + 6 · x + 10

y = 3 · (x² + 2 · x + 10 / 3)

y = 3 · (x² + 2 · x + 1) + 7

y - 7 = 3 · (x + 1)²

Case 9

y = 5 · x² + 40 · x - 6

y = 5 · (x² + 8 · x - 6 / 5)

y + 5 · 16 = 5 · (x² + 8 · x + 16) - 6

y + 86 = 5 · (x + 4)²

Case 10

y = (x + 5) · (x - 9)

y = x² - 4 · x - 45

y + 4 = (x² - 4 · x + 4) - 45

y + 49 = (x - 2)²

Case 11

y = (x - 4) · (x + 10)

y = x² + 6 · x - 40

y + 9 = (x² + 6 · x + 9) - 40

y + 49 = (x + 3)²

Case 12

y = (x + 2) · (x + 10)

y = x² + 12 · x + 20

y + 16 = x² + 12 · x + 36

y + 16 = (x + 6)²

Case 13

y = (x - 2) · (x - 6)

y = x² - 8 · x + 12

y + 4 = x² - 8 · x + 16

y + 4 = (x + 4)²

Case 14

y = (x + 1) · (x + 4)

y = x² + 5 · x + 4

y + 9 / 4 = x² + 5 · x + 25 / 4

y + 9 / 4 = (x + 5 / 2)²

Case 15

y = (x + 4) · (x - 5)

y = x² - x - 20

y + 1 / 4 = (x² - x + 1 / 4) - 20

y + 81 / 4 = (x - 1 / 2)²  

Case 16

y = 2 · (x + 2) · (x + 4)

y = 2 · (x² + 6 · x + 8)

y + 2 · 1 = 2 · (x² + 6 · x + 9)

y + 2 = 2 · (x + 3)²

Case 17

y = x · (x + 6)

y = x² + 6 · x

y + 9 = x² + 6 · x + 9

y + 9 = (x + 3)²

Case 18

y = 3 · (x + 4) · (x - 8)

y = 3 · (x² - 4 · x - 32)

y + 3 · 4 = 3 · (x² - 4 · x + 4) - 3 · 32

y + 12 = 3 · (x - 2)² - 96

y + 108 = 3 · (x - 2)²

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Answer:

If the truck's value dropped 15% each year, after one year the value of the truck is 22000*(1-0.15) = $18700

After the second year, the value of the truck would be 18700*(1-0.15) = $15995

After the third year, the value of the truck would be 15995*(1-0.15) = $13596.75

Rounding the answer to the nearest dollar, the value of the truck after 3 years is $13597

The probability that you pick exactly 2 juniors is 15/30 x 14/29 x 13/28 x 12/27, or 0.081.

1. Probability of picking the first junior: 15/30

2. Probability of picking the second junior: 14/29 (14 remaining juniors out of 29 total students after the first pick)

3. Probability of picking the third non-junior: 13/28 (13 remaining non-juniors out of 28 total students after the second pick)

4. Probability of picking the fourth non-junior: 12/27 (12 remaining non-juniors out of 27 total students after the third pick)

Therefore, the probability of picking exactly 2 juniors is

15/30 x 14/29 x 13/28 x 12/27

= 0.081.

The probability of picking exactly 2 juniors out of 4 slips of paper from a hat with the names of all 30 students in your statistics class is 0.081. This is calculated by taking the probability of picking the first junior (15/30) and multiplying it by the probability of picking the second junior (14/29, since there are 14 remaining juniors out of 29 total students after the first pick), the probability of picking the third non-junior (13/28, since there are 13 remaining non-juniors out of 28 total students after the second pick), and the probability of picking the fourth non-junior (12/27, since there are 12 remaining non-juniors out of 27 total students after the third pick).

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The measurement of side AC in the given right triangle is 10.12 units.

A triangle having at least one angle measuring 90° is called a right triangle.

Given that, a triangle ABC, right-angled at A,

AB = 15 and BC = 18.1, we need to find AC,

Please refer to the figure attached,

Using Pythagoras theorem,

BC² = AB² + AC²

AC² = BC² - AB²

AC² = (18.1)² - 15²

AC² = 327.61 - 225

AC² = 102.61

AC = 10.12

Hence, the value of AC = 10.12

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We have to pay $129,216.31; $64,800.

Option (c) is correct.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is the interest on interest, and it is the mechanism that causes an investment to grow at an exponential rate.

To calculate the amount of money you will have in the investment plan after 18 years, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A is the final amount (the future value)

P is the principal, or the initial deposit, in this case $300

r is the annual interest rate, in this case 7% (expressed as 0.07)

n is the number of years, in this case 18

m is the number of times the interest is compounded per year. in this case 12 (monthly)

By using this formula, the final amount will be:

A = 300(1 + 0.07/12)^(12*18)

A = $129,218.51

To compare this amount to the total deposits made over the time period, we can calculate the total amount of money deposited by multiplying the deposit amount ($300) by the number of deposits made per month (12) by the number of years (18).

Total deposit = 3001218 = $64,800

Hence, we have to pay $129,216.31; $64,800.

Option (c) is correct.

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Emmy answered average of 60 out of 75 math problems correctly on the quiz she took last week, meaning she answered a total of 60 problems correctly.

60/75 = 0.8

0.8 x 75 = 60

Emmy took a math quiz last week and answered 60% of the 75 problems correctly. To calculate how many problems Emmy got correct, we need to divide 60 by 75, which gives us 0.8. Then, we multiply 0.8 by 75, which gives us 60. This means that Emmy correctly answered 60 out of 75 math problems on the quiz. This is equivalent to 60%, which is the percentage of problems she got correct. It is important to note that if Emmy had answered any more or any less problems correctly, the percentage of correct answers would have been different. Therefore, it is important to understand the relationship between percentages and total number of problems answered correctly in order to accurately calculate the number of correct answers.

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The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.

c. f(x)= x^3-4x^2+4x-16

The polynomial with the given roots is a cubic polynomial. To get the coefficients of the polynomial, we can use the factor theorem. The factor theorem states that if a polynomial has a factor (x - a), then a is a root of the polynomial.

Therefore, the polynomial with roots 4, 2i, and -2i is f(x) = (x - 4)(x - 2i)(x +2i)

Expanding this polynomial, we get f(x) = x^3-4x^2+4x-16

The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.

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The approximate measure of angle JGH is 70.5°.

According to this question, we have a right triangle in which lengths of its hypotenuse (GH), in centimeters, and one leg (JH) are known and we must determine the measure of an angle (∠JGH), in degrees. A representation of this triangle is included in the image attached below.

By trigonometry we have the following expression for the required angle:

cos∠GJH = HJ/GH               .......(1)

Given, HJ = 2, GH = 6

cos∠GJH = 2/6

     ∠GJH = [tex]cos^{-1}\frac{2}{6}[/tex]

                ≈ 70.529

The approximate measure of angle JGH is 70.5°.

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Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.

An introduction to mathematics tool is the number line, which is a visual integer depiction of real numbers. It is a representation of an intensity line. Each actual figure is taken to symbolize a point on the real number, or each precise figure is taken to symbolize a position. On a number line, distances between increments are equal. A line's numbers can only be answered in the way that is specified by those numbers. The question that corresponds with the number will define how it is used. B: Speak your mind.

Here,

Given :

Number are as follows : 221 ,543,28492 and 92349

Thus,

To find that the number is divisible by 3 but not 9.

So , as we know that sum of individual number of that number is divisible by 3 .

Then thw hole number is divisible by 3 .

So , we see 543 is divisible by 3 but not 9 .

Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.

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a number is  divisible by 3 if the sum of its digits is divisible by 3.

a number is  divisible by 9 if the sum of its digits is divisible by 3.

the  number  divisible by 3 but not by 9 is 543,  

Answer: It takes 3 years

Step-by-step explanation:

20 percent of 1000 is 200 so 1000-200=800.  Year 1

20 percent of 800 is 160 so 800-160=640.       Year 2

20 percent of 640 is 128 so 640-128=512.         Year 3

So in total in takes 3 years

Answer:

See photo

Step-by-step explanation:

Edmentum/Plato

The Sine Ratio is written as [tex]\frac{Perpendicular }{Hypoynuse}[/tex] , then the maximum possible value of a Sine Ratio is 1 .

What is Sine Ratio ?

In a Right Triangle , the Sine of angle is defined as the ratio of length of the opposite side divided by the length of the hypotenuse .

we know that the domain for the Sine function is ⇒ all real numbers ;

and the range of Sine function is ⇒  [-1,1] ;

so , from the range we can conclude that , the maximum value is 1 .

Therefore , the maximum value of Sine ratio is = 1 .

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If the business owner wanted to make the case that the workers are paid well, she would use the range of central tendency.

The range, D

You are undoubtedly most familiar with the mean, which is the arithmetic average and a measure of central tendency. It is extremely easy to calculate the mean. Simple addition and division by the dataset's observation count are all that are required to calculate the values. All data values are included in the mean calculation.

Finding a variable's maximum observed value (also known as the range) and deducting its least observed value will yield the range (the minimum).

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Answer:

-16

Step-by-step explanation: