Substitute the given values into the given formula and solve for the unknown variable. If​ necessary, round to one decimal place.

I=PRT​; I=1920​, P=24,000​, R=0.04 ​(Simple interest​ formula)

Answer:

1/6

Step-by-step explanation:

Let x = number.

3/4 x = 1/8

Multiply both sides by 8.

8 × 3/4 x = 8 × 1/8

6x = 1

x = 1/6

Answer: 1/6

The possible fraction n is n = 5/8

From the question, we have the following statement that can be used in our computation:

The fraction is between 1/2 and 3/4.

This fraction is represented by n

So, we have

n is between 1/2 and 3/4.

The fractions 1/2 and 3/4 can be rewritten as

1/2 = 4/8

3/4 = 6/8

This means that

n is between 4/8 and 6/8

The number 5 is between 4 and 6

So, we have

5/8 is between 4/8 and 6/8

This means that

n = 5/8

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Answer:

[tex]\huge\boxed{\sf x = 5}[/tex]

Step-by-step explanation:

g(x) = -3x + 8

Given that, g(x) = -7

-7 = -3x + 8

Subtract 8 to both sides

-7 - 8 = -3x

-15 = -3x

Divide -3 to both sides

5 = x

OR

x = 5

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex]y=2x+3[/tex]

Step-by-step explanation:

We know that [tex]m=\frac{5-3}{1-0}=2[/tex] and that the [tex]y[/tex] intercept is 3.

The perimeter of the original square is 36 ft.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Let the side of square is x,

When one side is increased by 5 ft, the side = 5+x,

And other side is decreased by 3 ft, the side = x-3.

Also given that, the area of rectangle = 84 square ft

The area of rectangle = length×width

84  = (5+x)×(x-3)

By solving the equation, the value of x is 9,

Therefore, the side of the square is 9 ft

Perimeter of the square = 4x = 4×9 = 36 ft

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Answer:

y=-2

Step-by-step explanation:

[tex]y^2+4y+4=0\\y^2+2y+2y+4=0\\(y^2+2y)+(2y+4)=0\\y(y+2)+2(y+2)=0\\(y+2)=0\\and \\(y+2)=0\\y=-2[/tex]

[tex]Proof:\\(-2)^2+4(-2)+4=0\\4+(-8)+4=0\\8-8=0\\0=0[/tex]

a) The value of b if the total number of students is 55 is; b = 8

b)i) Probability that the student passed both french and german is 19/55

ii) Probability that the student passed exactly one of the two subjects is; 36/55

A venn diagram is used to compare and contrast two different ideas.

We are given that;

Number of students that passed French only = 17

Number of students that passed German only = 11

Number of students that passed both French and German = 19

Number of students that did not pass any of the 2 subjects = b

Total number of students = 55

Thus;

a) To get the value of b that will represent the number of students who didn't pass any of the 2 subjects will be calculated as;

b = 55 - (17 + 11 + 19)

b = 8

b)i) To get the probability that the student passed both french and german is given by the formula;

P(Paased french and german) = Number that passed french and german/Total number of students = 19/55

ii) To get the Probability that tells us the student passed exactly one of the two subjects is;

(17/55) + (19/55) = 36/55

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The continuous rate of growth is 50 %,the initial population is 940 and at time t = 5 11451 bacteria will be there.

a)

A exponential function is represented as:

n(t) = n(0) e^kt

where k is the continuous rate of growth.

Given problem:

The number of bacteria in a culture is given by:

n(t) = 940 e^0.5t

on comparing k = 0.5

= 0.5*100%

= 50 %

b)

On comparing with exponential function with given function.

n(0) = 940

which is the initial population.

c)

At t = 5

n(5) = 940*e^0.5*5

= 940*e^2.5

= 940*12.1824

≈ 11451

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Answer:

winning a raffle ticket is more like to occur because there is much more chance (24tickets) to win

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A would be 1/4 because there are 2 multiples of 4 so it would be 2/8 which would simplify to 1/4

B would be 3/5 since it’s 3/5 possibilities

C would be 12/50 because it would simplify from 24/100 to that

D would be 19/20 because there are 38 strawberry chews and + 2 cherry chews = 40 so 38/40 or 19/20

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Answer:

£52 was the original price

Step-by-step explanation:

The number of people surveyed in the bar graph is 34

The visual display of data (often grouped) in the shape of vertical or horizontal rectangular bars, with the length of the bars corresponding to the measure of the data, is called a bar graph.

The number of people surveyed is calculated by adding up the frequencies of each bar

The frequency shows the number of people using cell phones starting from zero cell phone user which is 1 to 6 cell phone users which is 5

The calculation

1 + 5 + 6 + 8 + 9 + 5 = 34

Hence the number people surveyed is gotten to be 34

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Answer:

A

Step-by-step explanation:

hope this helps! :) Hope you have. a great day

Step-by-step explanation:

ok hope it will help you thanks for watching hope it will happen

Miguel has a higher unit rate of change than Donna because 53mph is greater than 48mph.

The unit rate is used to show the relationship between the variables illustrated. Since Miguel drove for 8 hours at a constant rate and drove a total of 424 miles. The rate will be:

= 424 / 8

= 53 miles per hour.

The unit rate for Donna will be:

Miles / Time

= 144 / 3

= 48 miles per hour.

Therefore, Miguel has a higher rate.

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Answer:

[tex]62[/tex]

Step-by-step explanation:

based on the given:

(Note: of ⟹ multiplication, percentage ⟹ ÷100, the number of marks he got in math more than English ⟹ the value he got in math minus the value he got in English)

Moving on, for math test:

80 × 92.5/100 = 74

For English test:

64 × 18.75/100 = 12

Now, the number of marks he got in math more than English ⟹ 74 - 12 = 62

Therefore, final answer is 62

Answer:

Step-by-step explanation:

The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. The calculation is as follows:

x = μ + (z)(σ) = 5 + (3)(2) = 11

The z-score is three.

The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation

z=x-u/o produces the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.

The average amount of time spent studying among graduate students at this​ student's school is between 17.3 and 22.5 hours per week. which is the correct interpretation would be option (A).

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations.

A graduate student wanted to determine the average time spent studying between many graduate students at her school. She took a random sample of graduate students from her school and obtained an hour per week.

In the context of the problem,

We are​ 99% sure that the average amount of time spent studying among graduate students at this​ student's school is between 17.3 and 22.5 hours per week.

Therefore, the correct interpretation would be option (A).

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Answer:

[tex]\frac{71}{40}[/tex]

or

71/40

Explanation:

[tex]\frac{3}{5} + \frac{7}{8} + \frac{3}{10}[/tex]

LCM (Least Common Multiple) of 5, 8, and 10 = 40

5 × 8 = 40

8 × 5 = 40

10 × 4 = 40

(8 × [tex](\frac{3}{5} )[/tex] ) + (5 × [tex](\frac{7}{8} )[/tex] ) + (4 × [tex](\frac{3}{10} )[/tex] )

[tex]\frac{24}{40} + \frac{35}{40} + \frac{12}{40}[/tex]

[tex]\frac{71}{40}[/tex]

Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

The expression x - 35 represents the discounted price before tax. The expression 0.12x represent the amount of sales tax.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression given which models the final price of a scooter with an instant rebate in a state that charges sales tax is:

⇒ 0.12x + (x - 35)

As per the given expression,

The discounted price before tax = x - 35

The amount of sales tax = 0.12x

Thus, the expression x - 35 represents the discounted price before tax and the expression 0.12x represent the amount of sales tax.

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Given are the number of pens and + in students bag.

We can see from the dataset graph that -

Therefore -

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Answer:

Step-by-step explanation:

the consecutive are 39,40,41 and the smallest here is 39

Hope this helped

The option that can be used to verify the trigonometric identity, [tex]tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)[/tex] is option C;

C. [tex]tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)[/tex]

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

[tex]tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)[/tex]

The half angle formula for tangent indicates that we get;

[tex]tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}[/tex]

[tex]\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}[/tex]

When η = 0, we get;

[tex]-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}[/tex]

Therefore;

[tex]tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}[/tex]

[tex]cot\left(x \right) = \dfrac{cos(x)}{sin(x)}[/tex]

[tex]tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}[/tex]

[tex]\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}[/tex]

[tex]\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)[/tex]

Therefore;

[tex]tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)[/tex]

The correct option that can be used to verify the identity is option C

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The degree of the quadratic equation, ax² +bx+c = 0 will be 2.

Any equation of the form  ax² +bx+c = 0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation. Any function of the form of the given form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that the equation is,

ax² +bx+c = 0

The highest power of the quadratic equation is the degree to that quadratic equation. The highest power of the given quadratic equation is 2.

Thus, the degree of the quadratic equation, ax² +bx+c = 0 will be 2.

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Answer:

5 and two ninths

Step-by-step explanation:

Answer:

4/3=4*3+3*3=12/9+7/9=19/9

Step-by-step explanation:

En fait il faut le mettre au même dénonminateur puis additionner les numérateur.

The following gives the variations:

m= -4p -----------> direct variation

r=9/t----------->indirect variation

n=(1/2)f----------->direct variation

u=2/z----------->indirect variation

The value of y when x=2 is -14

What are direct and indirect variations ?

One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.

When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.

m= -4p -----------> direct variation

r=9/t----------->indirect variation

n=(1/2)f----------->direct variation

u=2/z----------->indirect variation

General equation for an indirect variation:

y = k/x

substitute y=7 and x= -4

7=k/-4

k=7*-4 = -28

To find y when x=2:

Substitute x=2 and k=-28 into the equation

y=-28/2 = -14

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The correct way to model the equation -x + 8 = 7x + (-8) is given by the option shown as follows:

1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side.

The equation is modeled according to the signals of each coefficient, with:

The equation in this problem is given as follows:

-x + 8 = 7x + (-8).

Then the tiles of each term are:

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Answer:

2091

Step-by-step explanation:

[tex]1+3.5+6+\cdots+101 \\ \\ n=\frac{101-1}{2.5}+1=41 \\ \\ a=1 \\ \\ d=2.5 \\ \\ S=\frac{41}{2}[2(1)+(41-1)(2.5)] \\ \\ =2091[/tex]