Katie and Mina both commute to work. Katie's commute on the train takes 10 minutes more than one half as many minutes as Mina's commute by car. It takes Katie 30 minutes to get to work. Write an equation to determine how many minutes it takes Mina to get to work.

Answer:

h=-12

Step-by-step explanation:

h/6 -1 =-3

h/6= -2

h=-12

Answer:

Step-by-step explanation:

[tex]\tt \cfrac{h}{6}-1=-3[/tex]

Add 1 to both sides:-

[tex]\tt \cfrac{h}{6}-1+1=-3+1[/tex]

[tex]\tt \cfrac{h}{6}=-2[/tex]

Multiply both sides by 6:-

[tex]\tt \cfrac{6h}{6}=6\left(-2\right)[/tex]

[tex]\tt h=-12[/tex]

________________________

Hope this helps!

Answer:

Step-by-step explanation:

B and C

3 x 10-2 is 30,000 times less powerful than 9 x 10-2. If 3 x 10 towards the negative 2 power equals times as much as 9 x 10 to a second power, then

Another way to put it is 2 + 3 = 6. As we've seen, is equivalent to 2 3. The multiplier is the quantity that multiplies the number of these equal groups by the multiplicand, the quantity of items in each group.

Given that 10-2 is 1/100 and 10-2 is 100, we may rephrase the formulas as follows:

9 x 100 = 900

3 x 1/100 = 0.03

At this point the values are comparable:

How many times more than 0.03 is 900?

We may calculate it by dividing 900 by 0.03: 900 0.03 = 30,000

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Using the Rational Zero Theorem to find all real zeros for given expression are:

[tex]$-\frac{1}{3}, 1$$[/tex]

What is rational zero theorem?

The Rational Zero Theorem is a theorem in algebra that helps find possible rational zeros (roots) of a polynomial equation with integer coefficients. The theorem states that if a polynomial equation with integer coefficients:

ax^n + bx^(n-1) + ... + kx + l = 0

has any rational roots, then they must be of the form: p/q, where p is a factor of the constant term l, and q is a factor of the leading coefficient a.

To use the Rational Zero Theorem, we need to find all possible rational zeros of the polynomial:

[tex]$$3x^3 - 5x^2 + 7x + 3 = 0$$[/tex]

The possible rational zeros are given by:

[tex]$$\pm\frac{p}{q}$$[/tex]

where [tex]$p$[/tex] is a factor of the constant term 3 and [tex]$q$[/tex] is a factor of the leading coefficient 3. Therefore, the possible rational zeros are:

[tex]$$\pm 1, \pm 3, \pm \frac{1}{3}$$[/tex]

To find the real zeros, we can use synthetic division or long division to divide the polynomial by each of the possible rational zeros. After testing each possible zero, we find that the real zeros of the polynomial are:

[tex]$x=-\frac{1}{3}, x=1$$[/tex]

Therefore, the solution is:

[tex]$-\frac{1}{3}, 1$$[/tex]

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With the help of given angle elevation we can conclude that, the saguaro cactus is approximately 2.19 meters tall.

What is trigonometry?

Trigonometry is a branch of mathematics that focuses on the relationships between the sides and angles of triangles.

What is angle elevation?

Angle elevation, also known as angle of elevation, is the angle between a horizontal line and a line of sight (or direction) to an object above the horizontal line.

We can use trigonometry to solve this problem. Let's call the height of the cactus "h". Then we can set up the following equation:

tan(26.1) = h / 4.5

To solve for "h", we can first multiply both sides by 4.5:

4.5 * tan(26.1) = h

Using a calculator, we can evaluate tan(26.1) to be approximately 0.4877. Multiplying this by 4.5 gives:

h = 2.19465

Rounding to the nearest hundredth, we get:

h ≈ 2.19 meters

Therefore, the saguaro cactus is approximately 2.19 meters tall.

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The probability of you, Leonard, and Sheldon being chosen together is 1/1140.

Probability is calculated by the total number of ways an event can occur divided by the total number of possible outcomes.

In this case, the total number of ways three students can be drawn out of 20 is 20C3 or 1140.

The probability of selecting you, Leonard, and Sheldon out of the three spots is 1/1140, or approximately 0.000877 or 0.0877%.

Total number of students in physics department = 20.Number of student spots for a conference trip to Cancun = 3.The probability that you, Leonard, and Sheldon are chosen is equal to the total number of ways you, Leonard, and Sheldon can be chosen divided by the total number of ways 3 students can be chosen from 20 students.

The number of ways that you, Leonard, and Sheldon can be chosen is 1 since you all need to be chosen together.

The total number of ways that 3 students can be chosen from 20 students is given by 20C3 (the combination of 20 objects taken 3 at a time).20C3 = (20*19*18)/(3*2*1) = 1/140

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Rοunding tο the nearest whοle number, the area οf the actual game rοοm in square feet is 56 square feet.

Geοmetry is a branch οf mathematics that deals with the study οf shapes, sizes, relative pοsitiοns οf figures, and the prοperties οf space.

Tο find the area οf the actual game rοοm in square feet, we first need tο cοnvert the given dimensiοns frοm inches tο feet. Since there are 12 inches in a fοοt, we have:

Length οf rectangle = 2 inches ÷ 12 inches/fοοt = 0.1667 feet

Width οf rectangle = 4.5 inches ÷ 12 inches/fοοt = 0.375 feet

Next, we need tο find the area οf the rectangle in square feet using the scale οf 1 tο 30. This means that 1 inch οn the drawing represents 30 inches in real life. Tο cοnvert this tο feet, we divide by 12, sο 1 inch οn the drawing represents 2.5 feet in real life. Therefοre, we have:

Length οf rectangle = 2 inches × 2.5 feet/inch = 5 feet

Width οf rectangle = 4.5 inches × 2.5 feet/inch = 11.25 feet

The area οf the rectangle is:

Area = length × width = 5 feet × 11.25 feet = 56.25 square feet

Hence, Rοunding tο the nearest whοle number, the area οf the actual game rοοm in square feet is 56 square feet.

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Answer:

3cm

Step-by-step explanation:

Perimeter is the boundary or outer line of a shape

Rectangle has 4 sides.

2 sides of top and bottom, being the same size

And 2 sides of left and right sides being the same size.

Perimeter of Rectangle = 9+5+9+5 = 28

Regular Pentagon has 5 equal sides.

So perimeter is: 5+5+5+5+5 = 25

Difference is biggest take away smallest

Therefore 28-25 = 3

Answer = 3cm

Straight path without bends,

A line connects points in space,

End to end it goes.

A line is a fundamental concept in geometry and is defined as a straight, one-dimensional figure with no thickness or width that extends infinitely in both directions. Lines can be drawn and measured, and they play a crucial role in many geometric and mathematical concepts, including angles, shapes, and equations. In addition to being a key concept in mathematics, lines are also used in art, design, and architecture. In art, lines can be used to create shapes, texture, and movement, while in design and architecture, lines are used to create structure, define space, and create a sense of balance and proportion.

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Complete question:

Use the same syllable pattern to create an original haiku about the term line.

If Yolanda bought 1/4 lb. of turkey and 2/4 lb. of ham at store, then ounces of meat Yolanda buy at the store is 12 ounces.

We know that there are 16 ounces in one pound.

So, to convert fractions of a pound to ounces, we multiply the weight in pounds by 16.

Yolanda bought 1/4 lb. of turkey, which is:

⇒ 1/4 × 16 = 4 oz,

And Yolanda bought 2/4 lb. of ham, which is:

⇒ 2/4 × 16  = 8 oz.

So, Yolanda bought a total of ; 4 oz. + 8 oz. = 12 oz.

Therefore, Yolanda bought a total of 12 ounces of meat.

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Answer:

Step-by-step explanation:

34. To calculate how much of Archie's hourly income the $15 sales tax represents, we need to divide $15 by Archie's hourly wage:

$15 ÷ $10.25 = 1.46 hours

So the $15 sales tax represents 1.46 hours of Archie's hourly income.

35. To calculate how much of Jeff's hourly income the $15 sales tax represents, we need to divide $15 by Jeff's hourly wage:

$15 ÷ $4400 = 0.0034 hours

So the $15 sales tax represents 0.0034 hours of Jeff's hourly income.

36. The sales tax impacts Archie more than Jeff because $15 represents a larger proportion of Archie's income than Jeff's income. For Archie, $15 represents about 14% of his hourly wage, while for Jeff, $15 represents only about 0.03% of his hourly wage.

37. If the sales tax increases to 12%, Archie would need to pay an additional 2% in sales tax (12% - 10%). So the new sales tax on a $150 bill would be:

$150 x 0.12 = $18

And the amount of sales tax Archie would need to pay would be:

$18 x 0.45 = $8.10

To calculate the percentage of Archie's income that he would now pay in tax on his $150 bill, we need to divide $8.10 by Archie's hourly wage:

$8.10 ÷ $10.25 = 0.79 hours

So Archie would need to work 0.79 hours to pay the sales tax on a $150 bill. As a percentage of his income, this is:

(0.79 hours x 100) ÷ 19 hours (assuming a typical workweek) = 4.16%

So if the sales tax increases to 12%, Archie would need to pay 4.16% of his income in sales tax on a $150 bill.

38. Archie might make adjustments to his purchases if the sales tax increases to 12%. For example, he might choose to buy cheaper or less expensive food items to reduce the amount of sales tax he needs to pay. He might also choose to buy some items in bulk to take advantage of lower prices and reduce the frequency of his purchases.

39. To calculate how much of Jeff's income the $18 sales tax would represent at a 12% rate, we can use the same method as before:

$18 ÷ $4400 = 0.0041 hours

So the $18 sales tax would represent 0.0041 hours of Jeff's hourly income.

40. Jeff might not make any adjustments to his purchases if the sales tax increases to 12%. Because he has a much higher income than Archie, the increase in sales tax would represent a relatively small proportion of his income. He might choose to continue purchasing the same types of food and luxury items as before, without significantly altering his spending habits.

41. Archie is impacted the most by the sales tax increase because he has a lower income than Jeff, so the sales tax represents a larger percentage of his income. While both Archie and Jeff would need to pay the same amount of sales tax on a $150 bill, the impact of that sales tax is much greater for Archie than it is for Jeff.

Based on the given dataset, we cannot say whether the sample size is a problem or not. Therefore, it cannot be determined whether the sample size is a problem or not for the dataset for number 11.

Parametric statistical methods refer to the techniques that deal with populations with known parameters. These methods are used when a population's characteristics are known, such as the population mean and standard deviation.

For instance, the student's t-test, ANOVA, and the correlation coefficient are some of the most commonly used parametric tests.Parametric statistical methods usually prefer a sample size of ~30. However, in some situations, even small samples may be sufficient, depending on the size of the effect being measured.

The larger the effect size, the smaller the sample size required, and vice versa. For instance, if there is a large difference between the two groups being compared, a small sample size may be sufficient.

Consequently, whether the sample size is a problem or not for the dataset for number 11 cannot be determined based on this information because the sample size is unknown.

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Answer:

Step-by-step explanation:

To find the lower, middle, and higher quartiles of the given data set, we need to first order the data from lowest to highest:

5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 18, 19

The total number of values in the set is 12, so the middle value (or the median) will be the average of the 6th and 7th values:

Median = (9 + 10) / 2 = 9.5

To find the lower quartile (Q1), we take the median of the lower half of the data set, which includes the first six values:

Lower half: 5, 6, 7, 8, 9, 10

Q1 = median of the lower half = (7 + 8) / 2 = 7.5

To find the higher quartile (Q3), we take the median of the upper half of the data set, which includes the last six values:

Upper half: 12, 14, 15, 17, 18, 19

Q3 = median of the upper half = (15 + 17) / 2 = 16

Therefore, the lower quartile is 7.5, the middle quartile is 9.5, and the higher quartile is 16.

Using transformations, we can find that the graph J represents the correct graph of f(x) and h(x).

A transformation is a change to the graph of a parent function. Translations, reflections, and dilations are the three different forms of transformations. A function can be altered either vertically (affecting the y-values) or horizontally (affecting the x-values) (affects the x-values).

[tex]h(x) = (x + 1) (x − 3)[/tex]

[tex]= x^2 --3x + x-3[/tex]

[tex]= x^2- 2x - 3[/tex]

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x) = 2x

Now, for  [tex]x = 0, f(x) = 0[/tex] and  [tex]h(x) = 0[/tex]

Therefore, both the graphs h(x) = 0trough the origin.

Now, for   [tex]x = 1, f(x) = 1[/tex]  and [tex]h(x) = 2[/tex]

Therefore, [tex]f(1) < h(1)[/tex]

Hence, the graph J represents the correct graph of f(x) and h(x).

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Finally, if the line has a slope of zero, it is a horizontal line. In this case, changing x will have no effect on y.

A graph is a data structure used to represent relationships or connections between objects. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices. The edges can be directed (pointing from one vertex to another) or undirected (not having a direction).

Graphs are used to model a wide range of real-world problems, such as social networks, transportation networks, computer networks, and many others. They are also used in computer science algorithms and data structures, such as shortest path algorithms, network flow algorithms, and data compression algorithms.

by the question.

The relationship between the change in x and the corresponding change in y on a graph depends on the slope of the line. The slope of a line is the ratio of the change in y to the change in x, and it represents how steep the line is.

If the line has a positive slope, that means it is slanting upwards from left to right. In this case, an increase in x will result in an increase in y, and a decrease in x will result in a decrease in y. The larger the slope, the more dramatic this effect will be.

On the other hand, if the line has a negative slope, it is slanting downwards from left to right. In this case, an increase in x will result in a decrease in y, and a decrease in x will result in an increase in y. Again, the larger the slope, the more pronounced this effect will be.

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a=d  1.co interior angle  2. are equal

b=c 1. co interior angle 2. are equal

A transversal that crosses two parallel lines creates alternate angles, which are a pair of angles. Alternative angles are often referred to as "Z-angles" or "alternate internal angles."

∠a=∠d (because co interior angle i.e, a and d are equal)

∠b=∠c (because co interior angle i.e, b and c are equal)

Both sides are parallel, so co interior angle rule satisfies.

Hence, a=d  1.co interior angle  2. are equal

b=c 1. co interior angle 2. are equal

Co-interior angles form between two parallel lines when a transversal crosses them. On the same side of the transversal, the two angles always sum to 180 degrees. Drawing a C shape helps us identify co-interior angles rather frequently. Only when both inner angles are 90 degrees are they equal.

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The three true statements about the two triangles are:
- Î"xyz is similar to Î"x'y'z'
- Angle xzy is congruent to Angle y'z'x'.
- The length of yx is twice the length of y'x'

1. Î"xyz ~ Î"x'y'z': The two triangles are similar because the reflection preserves the shape and the dilation with a scale factor of one-half changes the size proportionally.
2. Angle xzy ≅ Angle y'z'x':

Since the triangles are similar, their corresponding angles are congruent.

The reflection and dilation transformations do not affect the angle measures.
3. yx = 2y'x':

Due to the dilation with a scale factor of one-half, the corresponding side lengths of the triangles have a ratio of 2:1. So, the length of yx is twice the length of y'x'.

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Answer:

Step-by-step explanation:

To find the percentage decrease, we need to calculate the difference between the original price and the new price, and then express that difference as a percentage of the original price.

The difference between the original price of $115 and the new price of $69 is:

$115 - $69 = $46

To express this as a percentage of the original price, we need to divide the difference by the original price and multiply by 100:

($46 / $115) x 100% = 40%

Therefore, the percentage decrease in the price of the item is 40%.

Answer:

Step-by-step explanation:

51.1

Answer:

Step-by-step explanation:

answer: 51.1

The measure of the angle for the first circle is π/4 and the measure of the angle for the second circle is π. Since π is larger than π/4, we can conclude that the angle measure for the second circle is greater than the angle measure for the first circle.

The central angle of a circle is defined as the angle subtended at the center of the circle by an arc on the circumference. The measure of a central angle is proportional to the length of the arc it subtends, and the constant of proportionality is given by the formula:

angle measure = arc length / radius

Using this formula, we can find the measures of the central angles of the two circles:

For the first circle with radius 16 units and arc length 4π, the angle measure is:

angle measure = arc length / radius = (4π) / 16 = π/4

For the second circle with radius 5 units and arc length 5π, the angle measure is:

angle measure = arc length / radius = (5π) / 5 = π

Therefore, the measure of the angle for the first circle is π/4 and the measure of the angle for the second circle is π. Since π is larger than π/4, we can conclude that the angle measure for the second circle is greater than the angle measure for the first circle.

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Answer: 99 cm^2

Step-by-step explanation:

The easiest way to solve the surface area of these shapes is to draw a net of the shape and calculate the area of all the different shapes in the net.

Area for triangle: 1/2 * b*h - or for this shape just base times height because you have 2 triangles.

Area for rectangle: length times width.

The measurements I came up with are 15 for BOTH the triangles, 30 for one of the rectangles, 18 for the other, and 36 for the last rectangle which put together all equal to 99 cm^2.

Tell me if it works

Answer:

663

Step-by-step explanation:

SA= 2b+Ph= 2(1/2*6*2.5)+(6*3*6)(6)

Note that in the above equation, x = 5/7.

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 7:

7x/7 = 5/7

x = 5/7
x = 0.7142857143

Therefore, the solution set for the equation 7x = 5 is {5/7}. oro 0.7142857143

To show the solution set on a number line, we can mark the point 5/7 on the line: See the attached.

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Answer:

x=5, y=20

Step-by-step explanation:

3y+5+5y+15=180

8y=160

y=20

17x-70=2x+5

15x=75

x=5

Answer:

arc length ≈ 23.6 cm

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{1.25\pi }{2\pi }[/tex] ( r is the radius ) ( cancel 2π on numerator/denominator )

    = 2 × 3 × 1.25π

    = 7.5π

    ≈ 23,6 cm ( to the nearest tenth )

The size of the square that should be cut out of each corner to get a bin with maximum volume is 8 inches.

Let's assume that we cut out a square of side length x from each corner of the plastic piece. After cutting out the squares, the remaining length of the rectangle will be 32-2x inches, and the remaining width will be 42-2x inches.

The height of the bin will be x inches, since we fold up the flaps on each side.

The volume of the bin will be

V = (length) × (width) × (height)

= (32-2x) × (42-2x) × x

To find the value of x that maximizes the volume, we need to take the derivative of V with respect to x, set it equal to zero, and solve for x

dV/dx = 4x^3 - 148x^2 + 1344x

= 4x(x^2 - 37x + 336)

Setting this expression equal to zero and solving for x, we get

x = 8 inches, x = 21 inches, or x = 0 inches

However, x = 0 inches would result in no bin being formed.

To determine which value of x maximizes the volume, we need to evaluate V at each critical point

V(8) = 2688 cubic inches

V(21) = 1176 cubic inches

Therefore, the size of the square that should be cut out of each corner is 8 inches

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Answer: "A. 3/8"

Step-by-step explanation:

STEP 1: Determine the probability the spinner lands on a multiple of 3. To do this, write out the numbers on the spinner (1-8), and cross out every non-multiple of three (1, 2, 4, 5, 7, 8), this will leave the numbers 3 and 6 unmarked. This being said, 2/8 (1/4) of the numbers on the spinner are multiples of 3.

STEP 2: Determine the probability the spinner lands in a dark green region. In order to do this, write the numbers on the spinner out (1-8), and circle every number representing a dark green region (1, 3, 5, 7). This should leave four numbers (2, 4, 6, 8) un-circled, meaning 4/8 (1/2) of the numbers represent a dark green region.

STEP 3: Add the two answers together (1/4 + 1/2), and you should get the answer 3/8 (A).

NOTE: When adding fractions, make sure they have the same denominators. For example, in this problem, changing 1/2 to 2/4, and doing 1/4 + 2/4, instead of 1/4 + 1/2.

A grain οf salt is abοut 5 times as wide as a human cheek cell.

A standard fοrm οf a number in Maths is basically mentiοned fοr the representatiοn οf large numbers οr small numbers. We use expοnents tο represent such numbers in standard fοrm.

The cοrrect definitiοn οf standard fοrm cοuld be explained better in terms οf decimal numbers and fοllοwing certain rules. As we knοw, decimal numbers are the simplified fοrm οf fractiοns.

Sοme fractiοns give decimal numbers which have numbers after decimal at thοusandths, hundredths οr tenths place. But there are sοme fractiοns, which give a big decimal number. Tο represent such big numbers, we use simpler fοrms, which are alsο stated as Scientific nοtatiοn

Tο cοmpare the sizes οf the grain οf salt and the human cheek cell, we need tο divide the diameter οf the grain οf salt by the diameter οf the cheek cell:

[tex]\frac{(3*10^{-4} meters)}{(6*10^{-5 }meters)} \\\\=5[/tex]

Therefοre, a grain οf salt is abοut 5 times as wide as a human cheek cell.

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Answer:

Step-by-step explanation:

The length of side AB of the isosceles triangle is 8x + 5.

The formula for finding the length of a isosceles triangle side is given by:

Length of side = √x² +  y²

Where x and y are the lengths of the other two sides.

To find the length of the side AB, we need to first calculate x and y. We know that BC = 4x + 4 and CA = 3x + 9.

Therefore, [tex]x = BC - CA = 4x + 4 - 3x - 9 = x + -5[/tex]

And [tex]y = CA - BC = 3x + 9 - 4x - 4 = -x + 5[/tex]

Substituting these values in the formula, we get:

Length of side AB = √((x + -5)² + (-x + 5)²)

= √((x² + 25) + (x² + 25))

= √(2x² + 50)

= √(2(8x + 5)²)

= √(16x2 + 80x + 25)

= 8x + 5

Therefore, the length of side AB is 8x + 5.

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The image of point A after being reflected over the y-axis would have coordinates (2, 4).

When a point is reflected over the y-axis, it is essentially being flipped to the opposite side of the y-axis while remaining at the same distance from it.

In this case, point A has coordinates (-2, 4), which means it is located 2 units to the left of the y-axis and 4 units above the x-axis. When we reflect this point over the y-axis, its x-coordinate will change sign, meaning it will move 2 units to the right of the y-axis, while its y-coordinate will remain the same, meaning it will stay 4 units above the x-axis.

The point A has coordinates (-2, 4).

When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same.

Therefore, the image of point A after this transformation would have coordinates (2, 4).

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