Solve for the unknown quantity of x
15/2= 60/x

The equations have been computed below

3(x + 2) + 11 = 5(x - 4)

3x + 6 + 11 = 5x - 20

Collect like terms

3x - 5x = -20 - 17

-2x = -37

x = 37/2

x = 18.5

6x + 4 = 3(3 - 2x)

6x + 4 = 9 - 6x

Collect like terms

6x + 6x = 9 - 4

12x = 5.

x = 5/12

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Answer:

a) 16

b) 36

c) 4

d) 81

Explanation:

Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers. The square root of a number, n, written below is the number that gives n when multiplied by itself.

The volume of the pyramid is 576 cubic inches.

To find the volume of a square base pyramid, you can use the formula:

Volume = (1/3) x base area x height

In this case, the side of the square base is given as 12 inches, and the height is given as 12.5 inches.

First, calculate the base area of the pyramid:

Base area = side²

= 12²

= 144 square inches

Now, substitute the values into the volume formula:

Volume = (1/3) x 144 x 12.5

Volume = 576 cubic inches

Therefore, the volume of the pyramid is 576 cubic inches.

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y equals negative two thirds times x minus 2 is the equation of graph.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

The given two points are 3 comma 0 and 0 comma negative 2.

i.e (3,0)(0,-2)1)

The formula for slope is (y₂-y₁)/(x₂-x₁)

slope = (-2 - 0) / (0 - 3)

= -2 / -3

The negative negative are multiplied we get positive

= 2/3

The standard form of a line is y = mx + b, where m is slope of line and b is y intercept.

slope(m) = 2/3

We can use either of points (0,-2)...x = 0 and y = -2

now sub and find b, then y intercept

-2 = 2/3(0) + b

-2 = b

so  equation is : y = 2/3x - 2

Hence y equals negative two thirds times x minus 2 is the equation of graph.

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Answer:

-0.13333333333

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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9514 1404 393

Answer:

  (b)  Transitive property of congruence

Step-by-step explanation:

The relations involved are all congruence relations, eliminating choices A and C.

The symmetric property tells you ...

  if A ≅ B, then B ≅ A

It is not applicable in this case.

__

The applicable property is the transitive property of congruence:

  if A ≅ B and B ≅ C, then A ≅ C.

_____

Additional comment

This is similar to, but distinct from, the substitution property of congruence:

  if A ≅ B and A ≅ C, then B ≅ C.

Answer:

Transitive property of congruence

Step-by-step explanation:

Here

Hence

Option B

the answer is 16.77

fdmlksafndslakgfnlksdaajglsdanlkfsdalkfsad

The image is reflected over the y-axis. Then the correct option is B.

Given that:

Point of the polygon VWXYZ, W(2, 4)

Point of the polygon V'W'X'Y'Z', W'(-2, 4)

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

The point W' can be obtained by reflecting the shape across the y-axis.

Thus, the correct option is B.

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The missing diagram is given below.

There are 12 chaperones in total.

In molecular biology, molecular chaperones are proteins that help big proteins or macromolecular protein complexes fold or unfold conformationally. There are different groups of molecular chaperones, all of which have the same purpose: to help big proteins fold properly during or after synthesis as well as following partial denaturation. Protein translocation for proteolysis involves chaperones as well.

The first molecular chaperones to be identified are an assembly-type of chaperones that help nucleosomes form from folded histones and DNA.

Since heat stress increases the propensity for protein aggregation, one of the main roles of molecular chaperones is to prevent the accumulation of misfolded proteins. As a result, many chaperone proteins are categorized as heat shock proteins.

Chaperones and students combined: 3 + 20 = 23

by the number of individuals in total:

92 / 23 = 4

Divide that sum by the proportional number of chaperones:

4 x 3 = 12

There are 12 chaperones in total.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

wdym R6

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

6*2

Answer:

t = 1.399<1.710 ( from tabulated value)

we will accepted the null hypothesis

the marketing manager decides to carry out a test of hypothesis

H 0 : μ = 13.50

Step-by-step explanation:

Step1 :-

Given sample size 'n' = 25 customers

The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch.

therefore the population mean 'μ' = $13.50

A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be ¯ x = $ 14.50

sample mean ¯ x = $ 14.50

the restaurant informs the marketing manager that the standard deviation is σ = $ 3.50

Population standard deviation σ = $ 3.50

Step 2:-

we will use' t' test because of given small sample size is n=25

Null hypothesis: H₀ : μ= $ 13.50

Alternative hypothesis :H₁:μ ≠ $ 13.50

Degrees of freedom γ = n-1 = 25-1 =24

The test statistic 't' is

substitute all values , we get

t = 1.399

This is calculated value  t = 1.399

The tabulated value of t are 5% level with 24 degrees of freedom

t = 1.710

Step 3:-

t = 1.399<1.710

Since calculated value < The tabulated value of t are 5% level with 24 degrees of freedom.

we will accepted the null hypothesis

the marketing manager decides to carry out a test of hypothesis

Answer:

Sheryl rode 497/10 = <<497/10=49.7>>49.7 kilometres each day.

You can round this number to the nearest whole number by looking at the hundredth's place. Since the hundredth's place is 7, you can round 49.7 up to 50. Therefore, Sheryl rode approximately 50 kilometres each day.

Step-by-step explanation:

The velocity experimented by the car is equal to - 1 feet per second.

Herein we have the graph of the position of the car (y), in feet, versus time (t), in seconds. The graph shows a linear equation, that is, the position is described by a polynomial of the form:

y = m · t + b

Then, the functions for the velocity and acceleration are shown below:

Velocity

dy / dt = m

The slope represents the velocity of the car.

Acceleration

d²y / dt² = 0

Then, the velocity of the car is found by means of the secant line formula:

dy / dt = (0 ft - 10 ft) / (10 s - 0 s)

dy / dt = - 1 ft / s

The velocity of the car is - 1 feet per second.

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Answer:

B. 6/9 - 4/9

Step-by-step explanation:

Make sure each fraction has a common dominator

2/3 *3/3 = 6/9

4/9 = 4/9

6/9 - 4/9 = 2/9

Answer:

6/9 - 4/9, B

Step-by-step explanation:

the volume of a cilinder is:

So we can replace the radius and the high so:

Now we can replace pi by 3.14 so:

Answer:

D 41

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180 degrees.

so, we have already 35 for one angle, that leaves 145 for the other two.

x + 2 + 2x + 20 = 145

3x + 22 = 145

3x = 123

x = 41

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

To solve this problem, we need to use vector addition to find the resultant velocity of Julia.

Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.

The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.

The velocity of the river is 3 km/hr in the negative y-axis direction.

To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.

Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:

|V| = √(Vx² + Vy²)

where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.

Vx = 8 km/hr

Vy = -3 km/hr

|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr

The direction of the resultant velocity can be calculated as:

θ = tan⁻¹(Vy / Vx)

θ = tan⁻¹(-3 / 8) = -20.56°

The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).

Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).

Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)

Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Step-by-step explanation:

Yo all ✌️✌️

Jóin me

g-meet

besmfyotjp

Answer:

73.66 miles per hour

or if 40 degree whole swing of pendulum then ;

147.33 miles per hour.

Divide by 3600 for p/second

Step-by-step explanation:

sin x = opp /hyp  = 8 x sin (20) = 1.113384808 = 1.11ft

1.1ft p/s

5290 feet in every mile

5290/1.113384808 = 4751.27733 feet

3500 seconds in an hour

3500/4751.27733 x 100 = 73.6644013 m/ph

Scenario 2

or 2.2 feet per second depending on whether the angle from central each side is 20 degrees = 1.1 x 2 = 2.2 feet.

5290/2.22676962 =2375.63866

3500 seconds in an hour

3500/2375.63866 x 100 =  147.328803 m/ph

The sample of 3 seventh graders who own a bracelet out of 30 seventh graders does not closely estimate the thirty percent of all seventh graders owning bracelets.

Percentages are fractions where the denominator is 100.

We have,

Number of seven grade students = 30

Number of students who own a bracelet = 3

The percentage of seven grade student who owns a bracelet:

= (3 / 30) x 100

= (1/10) x 100

= 10 %

This means that 10% of seven grade student owns a bracelet.

Thus, the sample does not closely estimate the percentage of seventh graders who owns bracelets.

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Answer:

-64

Step-by-step explanation:

-9(5-2) -111÷3

PEMDAS says parentheses first

-9(3) -111÷3

Then multiply and divide from left to right

-27 -111÷3

-27 -37

Now add and subtract from left to right

-64

Answer: Less than 470 minutes

Step-by-step explanation:

This equation represents this problem.

0.04x + 44.4 = 0.06x + 35

Solve,

0.02x = 9.4

1 / .02 = 50

x = 470

At 470 minutes they're equal and we are looking for when Plan A is cheaper then Plan B, so x < 470

Use m instead of x in this problem, sorry didn't read the last line.

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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