Question 1-1
Look at the geometric sequence.
8, 64, 512, 4,096, ..
What is the seventh term in the sequence?
O 32,768
O262, 144
O2,097, 152
o 134, 217, 728

Answer:

2 1/4

Step-by-step explanation:

I know bc its basic math

Answer:

1: B

2: A

3: D

4: A

5: A, B

Step-by-step explanation:

1: 6/5 is 1.2 2/10 is 1/5

2: 6/14= 3/7 or 6/14

3: 3/12 is 1/4 or 3/12

4: 28/13 is 2 2/13

5: 35/6 which is also 2 3/16

#/# means divide so 35/6 is 35 divided by 6

Answer:

10%

Step-by-step explanation:

percent error: p

44 - 40 = 4

4/40 × 100 = p

p = 0.1 × 100

p = 10%

Percent error is 10%

The independent and dependent variables in this function are order p Variable

Mathematically, discrete random variables are stated to be impartial if: P(X=x, Y=y) = P(X=x) P(Y=y), for all x,y. Intuitively, for impartial random variables understanding the price of one in every of them, does now no longer extrade the chances of the opposite. The impartial variable is the cause. Its price is impartial of different variables for your study.

The structured variable is the effect. Its price relies upon on adjustments withinside the impartial variable.An impartial variable is precisely what it sounds like. It is a variable that stands on my own and isn't always modified with the aid of using the opposite variables you are attempting to measure. For example, a persons age is probably an impartial variable.

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Answer:

b. r = 18%

Step-by-step explanation:

0.3(0.82)^x:

0.3(0.82)^x:

The 0.82 is getting affected since it is raised to the power of x

Hence, for every iteration of x, the object is becoming 82% of itself.

100%-82%=18%

r = 18% ==> b

Option B is correct, 18% is the  rate of decay of the exponential function f(x) = 0.3(0.82)ˣ

A relation is a function if it has only One y-value for each x-value.

The exponential function f(x) = 0.3(0.82)^x can be written in the form f(x) = a(b)ˣ, where a = 0.3 and b = 0.82.

In an exponential function of the form f(x) = a(b)ˣ

the base b represents the rate of change.

If b is between 0 and 1, then the function represents exponential decay. The rate of decay r can be found using the formula:

r = (1 - b) x 100%

In this case, b = 0.82, so the rate of decay is:

r = (1 - 0.82) x 100%

= 0.18 x 100%

= 18%

Hence, option B is correct, 18% is the  rate of decay of the exponential function f(x) = 0.3(0.82)ˣ

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The money Trevor's family spend, in total, on shower water in the past month is $14.4

Two or more expressions with an Equal sign is called as Equation.

Given that the Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms.

In the past month, each person showered for an average of 480 minutes

an average 72 liters of shower water (over the entire month)

The cost of water per litre is 0.20 dollars.

We need to find the money Trevor's family spend, in total, on shower water in the past month

Cost of water used per minute = Water used by each person per month / Time each person spent bathing × Cost of water per liter

= 72 / 480 × 0.20

= 0.15 × 0.20

= $0.03.

Now 0.03×480=14.4.

Hence, 14.4 is the money Trevor's family spend, in total, on shower water in the past month.

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Based on the rate of change, Zehra is buying 7 cans per week.

The rate of change gives the ratio between the change in one quantity to the change in another quantity.

Linear relationships have a constant rate of change and the rate of change is usually represented as the slope or gradient.

For instance, the number of cans changed from 29 to 57, a difference of 28, as the number of weeks changed from 5 to 9, a difference of 4.

The rate of change can be expressed as 28/4 or 7.

The number of cans after 5 weeks = 29

The number of cans after 9 weeks = 57

The change in weeks = 4 (9 - 5)

The change in the number of cans = 28 (57 - 29)

The rate of change = 7 (28/4)

Thus, we can conclude that Zehra buys 7 cans weekly.

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The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

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Answer:

22

Step-by-step explanation:

Y is midpoint of WR.

Hence,

YR = 1÷2 of WR ( Half of WR )

So,

WR = 2YR

= 2×11

= 22

The equivalent to 5a³ + 4a³ is (5+4) a³, according to the question.

What do you mean by Equivalent ?

Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.

According to the given question,

We have the given options are:

O (5+4) a³+3

O (5+4) a³

O (5.4) a³+3

O (5.4) a³

Now, we will find the equivalent,

5a³ + 4a³

Then, we will taking common factor from the given equation:

5a³ + 4a³

= a³(5+4)

So that is same as (5+4)a³.

Therefore, the equivalent to 5a³ + 4a³ is (5+4) a³.

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Answer: Y=mx+b

Step-by-step explanation:

The original price of the instrument is $60.

Discount Price:

50% of 120 = 50/100 * 120

                   = 0.5 * 120

                   = 60

Original Price = Sale Price - Discount Price                  

                       = 120 - 60

                       = 60

Therefore, the original price of the instrument is $60.

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The simplest form of Sin 30° x tan 60° is √3/2 or sin  60° or cos 30°.

What are trigonometry ratios?

Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

Given that the trigonometry function is

sin 30° x tan 60°

Putting sin 30° = 1/2 and tan 60° = √3

=  (1/2) ×√3

=  (1/2) ×(√3/1)

Now multiply the denominators and numerators:

= √3/2

Putting √3/2 = sin 60°

= sin 60°

Again sin 60° = cos 30°

= cos 30°

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Given that the side lengths of the ramp are 10 feet, 2.5 feet, and 10.5 feet.

We know that for making a right angle A Pythagoras triplet must follow

So, a² + b² = c²

Where a, b, c are the lengths of the triangle and a, b <=c

So, on applying the above formula

We have,

2.5² + 10² = 10.5²

6.25 + 100 = 110.25

But 106.25 is not equal to 110.25

So all these sides are not good for making the ramp safe.

There are three types of the triangle based on angle -

1. Acute angled triangle

2. Right-angled triangle

3. Obtuse angled triangle

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Answer: point form: (4,3) equation form: x=4 y=3

Step-by-step explanation:

The answer is that a risk matrix/heat map has two factors namely, likelihood and Potential Impact on its x-axis and y-axis respectively.

What is a Risk map ?

A risk heat map is a tool used to present the results of a risk assessment process visually and in a meaningful way. Risk assessment is a critical step in risk management. It involves evaluating the likelihood and potential impact of identified risks.

Risk maps are a way of representing the resulting qualitative and quantitative evaluations of the probability of risk occurrence and the impact on the organisation in the event that a particular risk is experienced.

Organisations generally map risks on a heat map using a ‘residual risk’ basis that considers the extent to which risks are reduced by risk response strategies.

So, a risk matrix/heat map plots threats on a two-dimensional grid to assess qualitative risk. it has two factors as its x and y axes , Likelihood and Potential Impact respectively.

Please find the attached image.

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Answer:

87

Step-by-step explanation:

12x7+4-1/1

Answer: 741

Step-by-step explanation:

The biggest number Sam can make is 741. He can make this number by using the brackets and the division symbol: (12 + 1 + 1) / 4 = 741.

Answer:

57.5 milkshakes

Step-by-step explanation:

To find the number of milkshakes the ice cream shoppe sold in one hour, you can use the given information to set up the following equation: 15/4 = 71.25/X. Solving for X, we get X = 71.25 * 4/15 = 57.5. Therefore, the ice cream shoppe sold 57.5 milkshakes in one hour.

19

Step-by-step explanation:

15/4= 3.75

71.25 / 3.75=19

Answer:

Below

Step-by-step explanation:

Area = pi r^2

r = sqrt ( area/pi) = sqrt( 676 ) = 26

Circumference = pi d  = 2 pi r  = 2 pi (26) = 163.4 mm

The function g(x) = (x - 5)² has a translation of 5 units to the right.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over x-axis, (-x, y).

-f(x) = Reflection over y-axis, (x, -y).

The parent function is a quadratic f(x) = x².

Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.

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Answer:

[tex]x < -7[/tex]

Step-by-step explanation:

First subtract 2 from both sides.

[tex]-5x+2-2 > 37-2[/tex]

[tex]-5x > 35[/tex]

Then divide both sides by -5.

[tex]\frac{-5x}{-5} > \frac{35}{-5}[/tex]

For x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

Given is the inequality as follows -

- 5x + 2 > 37

The given inequality is -

- 5x + 2 > 37

- 5x + 2 > 37

- 5x + 2 - 2 > 37 - 2

- 5x > 35

x < - 7

Therefore, for x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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a. Using the graph, the estimated solution is: (-2, -0.6).

b. Solving algebraically, the exact solution is: (-2, -4/6).

The solution 0f a system of equations is that point of intersection where the lines of the two equations meet when they are plotted on a graph.

a. Given the graph of the equations, 2x - 3y = -2 and x + 1.5y = -3, the estimated solution, which is the point of the intersection of both lines can be, (-2, -0.5)

b. To get the exact solution, we would solve algebraically as shown below:

2x - 3y = -2 --> eqn. 1

x + 1.5y = -3 --> eqn. 2

Rewrite eqn. 2:

x = -3 - 1.5y --> eqn. 3

Substitute the value of x into eqn. 1:

2(-3 - 1.5y) - 3y = -2

-6 - 3y - 3y = -2

-6 - 6y = -2

-6y = -2 + 6

-6y = 4

y = 4/-6

y = -4/6

Substitute the value of y into eqn. 3:

x = -3 - 1.5(-4/6)

x = -3 + 1

x = -2.

The exact solution is (-2, -4/6).

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A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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The correct answer is C.

The smallest number of bags to cover the circular field is 3.0 pounds.

Area of a circle.

A circle is a shape that has a curved sides referred to as a  circumference. Its area can be determined by;

Area of a circle = [tex]\pi r^{2}[/tex]

where r is the radius of the circle

So that,

the radius of the circular field = 290/ 2

                                                 = 145 feet

The area of the circular field =  [tex]\pi r^{2}[/tex]

                                              = 22/7 x (145)(145)

The area of the circular field = 66078.57 square feet.

Given a bag has a capacity of 50 pounds, and that one pound of grass seed covers about 400 square feet.

Then,

total pounds in a bag = 50 x 400

                                    = 20000 pounds

the number of bags of grass seed needed = 66078.57 / 20000

                                                        = 3.304

The number of bags of grass seed needed = 3.30

Thus, the smallest number of bags the groundskeeper must buy to cover the circular field is 3.0 bags.

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z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

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The Yolanda's taxable income is $62,500.

What is income tax?

An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.

Given:

In 2008, Yolanda paid $3,875 in Social Security tax.

The Social Security tax rate was 6.2% to the maximum income of $94,200 that year.

Lets assume Yolanda´s income be `x`.

Now, calculating the taxable income of Yolanda

6.2% x (x) = 3875

[tex]\frac{6.2}{100} (x) = 3875\\x = 3875(\frac{100}{6.2}) \\x = 62500[/tex]

Hence, the Yolanda's taxable income is $62,500.

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The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width.  The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width

The area of the rectangle is the floor space the rectangle can occupy at a given time.

The given parameters are

L= 2w+5

The width = w

Then area is given by the formula

A=L*W

A=2w*w+5

Simplify the expression you have

A=2w²+5 where w is the width

Therefore the area is b. 2w²+5, where w is the width

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