A number is multiplied by 4. That result is added to 12. The final number is 40.
What is the original number?

A. Using percentages, if Drew earned 50% of $150 in the first week, the total amount earned is $75.

B. If Drew earned 50% of $75 in the second week, the total amount earned is $37.50.

C. If Drew earned 50% of $37.50 in the third week, the total amount earned is $18.75.

D. The percentage Drew earned in the fourth week is 12.5%.

The percentage refers to a relative size or ratio of one quantity compared to another larger quantity.

The percentage is a fractional value that shows the quotient of a division operation between the numerator and the denominator, which is then multiplied by 100.

A) The total goal for Drew to earn in four weeks = $150

The percentage earned in the first week = 50%

50% of $150 = $75.

B) The remaining part of the goal to be achieved after the first week = $75 ($150 - $75)

The percentage earned in the first week of the remainder = 50%

50% of $75 = $37.50

C) The remaining part of the goal after the second week = $37.50

The percentage of earnings in the third week = 50% of $37.50

= $18.75

D) Total earnings from week 1 to week 3 = $131.25 ($75 + $37.50 + $18.75)

$131.25/$150 x 100 = 87.5%

Remaining percentage = 12.5% (100 - 87.5)

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When you have a system of linear equations, and you identify terms with the same variable and same coefficients, you can use the subtraction method to obtain an equation in which you can obtain the value of one of the variables.

Answer:

x = 50

Step-by-step explanation:

Thus, we can find the value of x proving the horizontal lines are parallel by setting the two expressions representing the measures of angles 3 and 7 equal to each other:

(3x - 20 = 2x + 30) + 20

(3x = 2x + 50) - 2x

x = 50

Thus, 50 is the value of x proving that the horizontal lines are parallel.

The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

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a rule in quadratic equ states that

if summation of the roots should be -b/a of the equa

comparing the equ x² - 6x + y=0

with. ax² + bx +c =0

we see that in the equ, a= 1, b=-6

so the sum of the roots is -(-6)/1= +6

looking the the option the only one that agreed is option A

-2 + 8= 6

there fore the values of x are -2 or 8

a) The relation is reflexive, symmetric, and transitive.

b) The relation is not reflexive, symmetric, or transitive.

a) For each watermelon x, x is related to x because the measured weight of x is at least the measured weight of x. Therefore, the relation is reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is also related to x (meaning the measured weight of y is at least the measured weight of x). Therefore, the relation is symmetric.

For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is related to z (meaning the measured weight of x is at least the measured weight of z). Therefore, the relation is transitive.

b) For each watermelon x, x is not related to x because no two watermelons have the same measured weight. Therefore, the relation is not reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is not related to x (meaning the measured weight of y is not at least the measured weight of x).

Therefore, the relation is not symmetric. For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is not related to z (meaning the measured weight of x is not at least the measured weight of z).

Therefore, the relation is not transitive.

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The roots of the equation will be imaginary. Then the number of real solutions will be zero.

The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as

D = b² - 4ac

The type of roots will be given below.

The equation is given below.

x² + 4x + 5 = 0

The discriminant of the given equation will be

D = 4² - 4 x 1 x 5

D = 16 - 20

D = - 4

D < 0

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

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Answer:

Step-by-step explanation:

Given function:

Convert the equation into vertex form:

Vertex is (2, 4) at which the minimum y-value is 4

Correct choice is C

Answer:

sin a = -3/5

Step-by-step explanation:

sin^2(a)+cos^2(a)=1

sin^2(a)+ (4/5)^2 = 1

sin^2(a) = 1 - 16/25 = 9/25

sin a = 3/5 ( in Quadrant 1)

In quadrat IV the sine is negative

so sin a = -3/5

Answer:

p = 73.21 pounds of strawberries

Step-by-step explanation:

M + 10 = 5.6p - 96

314 + 10 = 5.6p - 96

314 +96 = 410

410 = 5.6p

410/5.6 = p

73.2142857143 = p

p = 73.2142857143

Answer:

75 pounds

Step-by-step explanation:

Replace M in the equation with 314

314 + 10 = 5.6p - 96

324 = 5.6p - 96

5.6p = 324 + 96

5.6p = 420

Divide both sides by 5.6

p = 75

The random variation that occurs in any time series is called the irregular component.

The irregular component refers to the random fluctuations or unpredictable patterns that are observed in a time series. It represents the unexplained variability in the data that cannot be attributed to any identifiable pattern, such as seasonal patterns, cyclical effects, or trends. It is often characterized by short-term fluctuations that occur randomly and do not follow a specific pattern or trend.

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The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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The full scope of her survey or the methodology she used to collect her data.

According to Kierra's survey results, it seems that the number of females attending summer camp is slightly higher than the number of males. To complete the table for her survey results, we can use the following information:
- In the "Gender" column, we can write "Male" and "Female" to represent the two categories Kierra surveyed.
- In the "Number of Participants" column, we can fill in the values that Kierra collected from her neighborhood.

For example, if she surveyed 100 people and found that 40 of them were males attending summer camp, we can write "40" in the row for "Male" under the "Number of Participants" column.
- We can then add up the values in each row to find the total number of participants in each category. For example, if Kierra found that 60 females attended summer camp, we can write "60" in the row for "Female" under the "Total" column.
| Gender | Number of Participants | Total |
|--------|----------------------|-------|
| Male   | 40                   | 100   |
| Female | 60                   | 100   |
It's important to note that this is only a small part of Kierra's survey results, and we don't know the full scope of her survey or the methodology she used to collect her data.

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Step-by-step explanation:

Line AB has a Slope of -20/5 or -4. Since the line that is being calculated is parallel it has the same slope. We can plug this Slope and the given point of the line into the point Slope equation for an equation of y - 3 = -4 (x + 1).

Answer: No real solutions

Step-by-step explanation: to solve for x and find a solution you need to take the square root of -144

This is not possible as this a negative number . There is a solution if we use complex numbers, but this not included in the question

Answer:

D

Step-by-step explanation:

Answer:d

Step-by-step explanation:

D

The slope of the line is  0.64

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

Slope = rise/run

          = 3.2/5

          = 0.64

Thus the slope of the line is  0.64

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Answer:

42.3

Step-by-step explanation:

Answer:

May be the ans is option C and A

The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.

In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.

The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.

By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.

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Andrea's production will be more efficient if we produce chairs, and Jana's production will be more efficient if we produce scarfs. the combination of 18 chairs and 16 scarfs is efficient and attainable. Answer: D. 16 chairs and 11 scarves.

Opportunity cost means the cost of a foregone alternative, which is incurred by choosing one option over the other. It is essential to minimize opportunity costs when making decisions about production and consumption. Let us calculate Liam, Andrea, and Jana's opportunity costs per item:1. Liam produces 1 scarf in 120 minutes and 1 chair in 120 minutes. Therefore, Liam has an opportunity cost of 1 chair for each scarf. 2. Andrea produces 1 scarf in 80 minutes and 1 chair in 60 minutes. Andrea's opportunity cost of producing 1 scarf is 3/4 chairs, and her opportunity cost of producing 1 chair is 4/3 scarves. 3. Jana produces 1 scarf in 60 minutes and 1 chair in 30 minutes. Jana has an opportunity cost of 1/2 chairs for each scarf and 2 scarves for each chair.

We can tabulate the data as follows:WorkersOpportunity cost of 1 scarfOpportunity cost of 1 chairLiam1 chair1 scarfAndrea3/4 chairs4/3 scarvesJana2 scarves1/2 chairsTo determine which combinations of chairs and scarfs are efficient and attainable, we should consider each worker's opportunity cost. The lowest opportunity cost is the most efficient since it reflects the least sacrifice for the most significant gain. 1. Liam has the same opportunity cost for each item, and so, we cannot use his production. 2. Andrea's opportunity cost of producing a chair is less than Jana's.

Thus, we should produce items according to the most efficient worker until the opportunity cost increases and then switch to the next most efficient worker.Suppose we have eight hours of working time. Liam will produce 4 chairs, and Andrea will produce 6 chairs and Jana will produce 8 chairs. Thus, a total of 18 chairs can be produced. To calculate the scarfs produced, we should multiply the chairs produced by each worker by their respective opportunity costs for a scarf:Andrea: 6 chairs × 4/3 scarfs per chair = 8 scarfsJana: 8 chairs × 2 scarfs per chair = 16 scarfs.

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Answer:

L=6x^2-4x+5

P=12x^2-4x-2

Step-by-step explanation:

A=WL

So, we know the area is 6x^2-8x-30 and the width is 2x-6

Substitute

(6x^2-8x-30)=(2x-6)(L)

L=(6x^2-8x-30)/(2x-6

Divide

L=6x^2-4x+5

P=2L+2W

Substitute

P=2(6x^2-4x+5)+2(2x-6)

P=12×^2-8x+10+4x-12

Simplify

P=12x^2-4x-2

\( {3}^{ - 2} \times {3}^{ - 5} = {3}^{ - 7} \)

Answer:

A) 3^-7

Step-by-step explanation:

Answer:y=2x+-1

Step-by-step explanation:

y= slopex + y-intercept, the y-intercept is at the point (0,-1) as the y-intercept is when the x coordinate is 0 and the y coordinate gets touched by the y axis, therefore 2x+-1

The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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To evaluate the given expressions using the vectors ū = <6, 8> and v = -4i + 3j, we can perform vector operations like multiplication, find magnitude.

a) 2ū - 3v: Multiply each component of ū by 2 and each component of v by 3, then subtract the resulting vectors. The calculation yields 2ū - 3v = 2<6, 8> - 3(-4i + 3j) = <12, 16> - <-12, 9> = <12 + 12, 16 - 9> = <24, 7>.

b) ||ū||: To find the magnitude (length) of ū, use the formula ||ū|| = √(x^2 + y^2), where x and y are the components of ū. In this case, ||ū|| = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.

c) ||ū + v||: Add the corresponding components of ū and v, then find the magnitude of the resulting vector. Calculation: ||ū + v|| = ||<6, 8> + (-4i + 3j)|| = ||<6 - 4, 8 + 3>|| = ||<2, 11>|| = √(2^2 + 11^2) = √(4 + 121) = √125 = 5√5.

Therefore, the evaluations are: a) 2ū - 3v = <24, 7>, b) ||ū|| = 10, c) ||ū + v|| = 5√5.

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Some important concept before solving answer :-

\( \\ \)

When ever there is three dimensional figure remember, where one figure is related to other then there's always relation with volume.

So it may get pretty difficult to understand therefore I am dividing into small parts for better understanding.

\( \\ \)

\( \pmb{ \bf \dag\cal{Part \ One:}}\)

As we know there will be relation of volume, so let's find volume of the cone first.

\( \\ \)

Given :-

⭑Height = 10 cm

⭑radius = 3cm

\( \\ \)

To find :

⭑volume of cone

\( \\ \)

Let represent :-

⭑Height as : h

⭑radius as : r

⭑volume of cone as : v

\( \\ \\ \)

Formula to find volume of cone :-

\( \\\)

\( \bigstar\boxed{ \rm v = \pi {r}^{2} \times \frac{h}{3} }\)

\( \\ \)

So let's find v!

\( \\ \)

\( \dashrightarrow\sf v = \pi {r}^{2} \times \dfrac{h}{3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7} \times {3}^{2} \times \dfrac{10}{3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7} \times {3} \times 3\times \dfrac{10}{3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7} \times {\cancel3} \times 3\times \dfrac{10}{\cancel3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times \dfrac{10}{1} \)

\( \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times10\)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22\times 3\times10}{7}\)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22\times 30}{7}\)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{660}{7}\)

\( \\ \\ \)

\( \dashrightarrow\bf v =94.3 {cm}^{3} \)

\( \\ \\ \)

\( \pmb{ \bf \dag\cal{Part \: \: Two:}}\)

So remember that cone filled with water is equal to volume of cone.

volume of water filled in cone = volume of water in cuboid.

So you probably thinking that above sentence is wrong , cause they haven't told volumes of cuboid and cone are equal, but we have to find depth of water filled not depth of cuboid.

\( \\ \\ \)

Given :-

⭑Volume of cuboid = 94.3 cm³

⭑Length of cuboid = 5cm

⭑Width of cuboid = 3cm

\( \\ \)

To find :-

⭑Depth of water in cuboid

\( \\ \)

Let represent:-

⭑Volume of cuboid as : V'

⭑Length of cuboid as : L

⭑Width of cuboid as : W

⭑Depth of water in cuboid as : D

\( \\ \\ \)

Formula to find volume of cuboid :-

\( \\ \\ \)

\( \bigstar\boxed{ \rm V'= W \times L \times D }\)

By using this formula we can find depth of cuboid.

\( \\ \\ \)

\( : \implies \sf V'= W \times L \times D \)

\( \\ \\ \)

\( : \implies \sf 94.3= D \times 3 \times 5\)

\( \\ \\ \)

\( : \implies \sf \dfrac{943}{10\times 3 \times 5} = D \)

\( \\ \\ \)

\( : \implies \sf \dfrac{943}{10 \times 15} = D \)

\( \\ \\ \)

\( : \implies \sf \dfrac{943}{150} = D \)

\( \\ \\ \)

\( : \implies \sf D = \dfrac{943}{150} \)

\( \\ \\ \)

\( : \implies \bf D = 6.3cm\)

\( \\ \\ \)

Required Answer:-

Depth = 6.3 cm

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Step-by-step explanation:

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You did it please don't delete