Here is the histogram of a data distribution. All class widths are 1

Which of the following numbers is closest to the mean of this distribution?

Answer:

equal to

Step-by-step explanation:

4 + 1/2= 4+ 0.5= 4.5

4.5=4.5

Answer:

Pedro can buy 4 pounds of pears and 3 pounds of apples.

Step-by-step explanation:

Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.

$2×3lb + $3×4lb=$18

Answer:

Step-by-step explanation:

1) sixty-seventh and nine hundred and twenty-five thousands

2)one-eighty two and fifty-one thousands

3)thirty-nine and thousand four thirty two thousands

4) eighty five and two sixty seven thousands

5) ninety seven and seven thousand and three-fifty two thousands

The minimum age of Johnny is 21 as calculated by linear inequality.

Let Johnny 's age be x.

hence bobby's age = (x+5)/2

Now the sum of their ages is over 66 years.

So we will set an inequality to find the minimum age of Johnny.

x + (x+5)/2 > 66

or, 2x + x + 5 > 66

or, 3x > 61

or, x > 20 1/3

Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:

A is smaller than b, as shown by the symbol a < b.

When the expression a > b is employed, it means that a is greater than b.

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Answer:

7/12

Step-by-step explanation:

12/12 - 5/12 = 7/12

The constant of proportionality of the equation y =−7.48​x is - 7.48.

Proportional relationships are relationships between two variables where their ratios are equivalent

In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.

Therefore, a proportional relationship is one in which two quantities vary directly with each other.

Hence, in mathematical form,

y ∝ x

y = kx

where

y varies directly as the variable x.

In the equation,

k = - 7.48

Therefore, the constant of proportionality  is - 7.48.

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Answer:

20

Step-by-step explanation:

Absolute value is the distance from zero. Absolute value is always positive.

| -20 | is positive. It is 20 units from 0. So it is 20.

| -20 | = 20

(Be careful, absolute value doesn't just flip the sign to the opposite.

| 20 | = 20 also because the distance from 0 to 20 is also 20.)

Answer:

See below

Step-by-step explanation:

The area (triangle) marked 'x' in the diagram below

Answer:

21 Assignments were NOT English.

If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.

Let x represent the weight of Cooper

Let x +25 represent the weight of Daisy

Let 3x -20 represent the weight of Luna

Hence,

x + (x +25) + (3x -20) = 175

5x +5 =175

Combine like terms

5x = 175 -5

5x =170

Divide both side by 5x

x = 170/5

x =34

Weight of Luna

3x -20  where x= 34

3(32) -20

= 102 -20

= 82 pounds

Therefore the correct option is D.

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Answer:Angles in a triangle may or may not be congruent.

The values of x and y are 90 and 47, respectively.

From the figure, we have:

This means that, angle x is a right-angle.

So, we have:

Triangle ABC is an isosceles triangle.

So, we have:

The measure of y is then calculated as:

--- sum of angles in a triangle

This gives

Subtract 137 from both sides

Hence, the values of x and y are 90 and 47, respectively.

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Step-by-step explanation:

The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.

AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.

In the given figure FE║GE means FE is parallel to GE.

so ∠EFS = ∠HGS

and ∠FES = ∠GHS

also ∠S is common for both.

If two triangles are similar then ratio of corresponding sides are also same.

So, by applying this

[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]

54/24 = FE/20

( 54*20 ) / 24 = FE

FE = 45m.

Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.

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Answer:

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

Correct choice is B.

Answer:

b)  -6

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given the interval is [-2, 0]:

Substitute the endpoints of the interval into the function and solve:

[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]

Answer:

  DNE

Step-by-step explanation:

You want to know the y-intercept of x = -4.

The y-intercept is the point where a graph crosses the y-axis.

The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.

There is no y-intercept. It does not exist (DNE).

Answer:

Step-by-step explanation:

Intrest = PRT\100

$1089. =. ($1100x12xR)\100

$1089. = 132R

 Divide through by 132.

R. =. 8.25%

Answer:

300/100%=3%

Step-by-step explanation:

sorry, can't explain.Ihave class tomorrow

The exponential function will be written as y = 14⁰.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,

[tex]y = ab^x \\[/tex]

14 = ab⁰

a = 14

The equation will be written as,

y = 14b⁰

y = 14⁰

Therefore, the exponential function will be written as y = 14⁰.

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The expression as power is written as 2¹⁰ and 2^9

The values are

power or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.

8• 2^7

= 2 * 2 * 2 * 2^7

= 2^10

= 1024

16•32

2^5 = 2 * 2 * 2 * 2 * 2

2^4 = 2 * 2 * 2 * 2

16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

= 2^9

= 512

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Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

According to the question,

We have the following information:

In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.

Now, let's take the principal amount to be $x.

We know that the following formula is used to find simple interest:

Simple interest = (principal*rate*time)/100

(x*2.5*8)/100 = 1270

Using the cross multiplication method:

20x = 127000

x = 127000/20

x = $6350

Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

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Answer: See coordinate graph below.

Step-by-step explanation: The black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

A': (1, -4)

Let me know if this is right! :)

The speed of the current is equal to 8 miles per hour.

Mathematically, speed of any physical object can be calculated by using this formula;

Speed = distance/time

Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:

Speed downstream = 14 + c.

Speed upstream = 14 - c.

Additionally, the total time would be given by:

Total time = total distance/speed

Time upstream + time downstream = 6.5 hours

33/(14 - c) + 33/(14 + c) = 7.0

Multiplying both sides of the equation by (14 - c)(14 + c), we have:

33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)

462 + 33c + 462 - 33c = 7.0(196 - c²)

924 = 7.0(196 - c²)

Dividing both sides of the equation by 7.0, we have:

132 = 196 - c²

Speed of the current, c² = 196 - 132

Speed of the current, c² = 64

Speed of the current, c = √64

Speed of the current, c = 8 miles per hour.

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Answer:

I think B. 3.85 units

Step-by-step explanation:

By the sequence of term to term rule the value of : a)  [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4    b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19     c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .

Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to

[tex]$$\mathrm{u}_0=1$$[/tex]

The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3

We have to simply put the value in their places to get the proper answer -

a). Put the [tex]$u_{n+1}=u_1$[/tex]

n+1 = 1  ⇒ n = 0

put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3

we wil get

[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4

b). Put the [tex]$u_{n+1}=u_2$[/tex]

n + 1 = 2 => n = 1

put  n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3

we wil get:

[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19

c). Put the  [tex]$u_{n+1}=u_3$[/tex]

n + 1 = 3 => n = 2

Put n=2 in the formula+3

we wil get :

[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364

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Answer: The answer to this question is $90.

Step-by-step explanation:

The Simple interest is $90.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5.

Given:

P= 1500

R = 12%

T= 6 month = 1/2 year

Using, formula of Simple Interest

I = P x R x T /100

I = 1500 x 12 x 1/ 2x100

I = 18000/200

I = 90

Hence, the interest is $90.

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The third term will be 5 in the explicit arithmetic sequence.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The formula to find the general term of an arithmetic sequence is,

aₙ = a₁ + (n-1)d

The explicit formula of an arithmetic sequence is given in the question as:

F(n) = 3n -4   ....(i)

To determine the term 3.

Substitute the value of n = 3 in equation (i),

T₃ = 3(3) - 4

T₃ = 9 - 4

Apply the subtraction operation,

T₃ = 5

Therefore, the third term will be 5 in the explicit arithmetic sequence.

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The percentages, using the Empirical Rule, are given as follows:

a) Between 106 and 124: 32%.

b) Between 88 and 160: 95%.

c) Between 70 and 124: 49.85%.

d) Above 160: 2.5%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The mean and the standard deviation in this problem are given as follows:

Considering the symmetry of the normal distribution, to facilitate the calculations, we have that:

160 is two standard deviations above the mean, hence the percentage above it is of:

2.5%.

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