A factory produces 70 toys per hour. The relationship between the number of toys produced, t, and the number of hours elapsed, h, is proportional. Which equation shows this relationship?

A. h = 70t
B. t=70h
C. h=70 + t
D. t = 70 - h

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer:

41.5

Step-by-step explanation

The equation is

X×65/100=27

x=27×100/65

x=27×20/13

x=540/13

x=41.5

Answer:

4

Step-by-step explanation:

8/2=4 (see pic below)

Answer: HEre finnaly this is right..

Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function?

0≤x≤8

Part B: What does the y-intercept of the graph of the function f(m) represent?

the length at the start of the study

Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent?

6.86−5.047−3=1.82

it represents the average growth in length of the fish from the 3rd month to the 7th month of the study

Step-by-step explanation:

Using the fact that all points on a circle are equidistant to its center, we will see that:

a =  -3 ±√21

All the points on a circle are equidistant to its center. Here the center is at (-3, -2), and we know that (0, -6) is on the circle.

The distance between these two is:

d = √( (-3 - 0)^2 + (-2 + 6)^2) = 5

Then the distance between (a, 0) also should be 5 units, so:

5 = √( (-3 - a)^2 + (-2 - 0)^2)

5 = √( (-3 - a)^2 + 4)

5^2 = (-3 - a)^2 + 4

25 - 4 = (-3 - a)^2

21 = (-3 - a)^2

±√21 = -3 - a

a = -3 ±√21

these are the two possible values of a.

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The surface area of this triangular prism is 784 sq cm.

Let's find rectangular areas first.

16×24 + 10×16

Adding both areas of both rectangles

384+160

= 544 sq cm

Now lets find the side triangles.

Area of triangle =1/2×base×height

Remove 1/2 because you have 2 triangles, 1/2×2 = 1

24×10

= 240

Total surface area =240 sq cm + 544 sq cm

= 784 sq cm.

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The volume of balloon A is \(\frac{2}{5}\) gallon and the volume of balloon B is \(\frac{1}{5}\) gallon.

What is volume?

Any three-dimensional solid's volume is simply the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.

We are given that two balloons have a total volume of \(\frac{3}{5}\) gallon.

Let the volume of balloon A be x and the volume of balloon B be y.

So, we get

x + y = \(\frac{3}{5}\)

Also, it is given that the difference of their volumes is \(\frac{1}{5}\) gallon and Balloon A has a greater volume than Balloon B.

So, we get another equation as

x - y = \(\frac{1}{5}\)

Now, on adding both the equations, we get

⇒ 2x = \(\frac{4}{5}\)

Now, on solving we get

⇒ x = \(\frac{2}{5}\)

Now, on substituting the value of x in the equation, we get

⇒ \(\frac{2}{5}\) + y = \(\frac{3}{5}\)

⇒ y = \(\frac{1}{5}\)

Hence, the volume of balloon A is \(\frac{2}{5}\) gallon and the volume of balloon B is \(\frac{1}{5}\) gallon.

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A distribution of scores on a driver's license test forms is normally shaped. This is an example of a symmetrical distribution is TRUE.

A symmetrical distribution is a distribution where there is an equal number of data points on both sides of the center point, in which the mean, mode, and median of a data set are all similar.

A normal distribution is a bell-shaped distribution that is symmetrical, with most of the data falling near the mean and progressively less toward the tails. When data are symmetrical, the mean and median values are similar, and the standard deviation can be used to compute the proportions of data within a range of values surrounding the mean.

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Question :

The sales tax rate in New Mexico is 5.125%. Select all the equations that represent the sales tax, t, you

would pay in New Mexico for an item of cost c?

A. t = 5.125c

B. t = 0.5125c

C. t = 0.05125c

D. t = c = 0.05125

(E. t = 5.025 c

 Answer:

C. t = 0.05125c

Step-by-step explanation:

First we have to understand the meaning of % sign. It is called percent or percentage. Where cent means 100. Now all we know that 100 cents make one dollar, that is why these 100 smaller units are called as cents.

Now if sales tax is 5.125 percent, remember that if there is $100 capital amount, it will be $5.125 tax.

Now how much would it be for $1?

simply, it will be $0.05125

Now for equation in option C

t = 0.05125 x 1

t = 0.05125

here you can see that the equation is satisfied.

So from this we can establish the equation that for any cost, the relation between tax and cost will be:

t = 0.05125c

The factorization of the polynomial b³-1000 is (b-10)(b²+10b+100).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is b³-1000.

Here, b³-1000=b³-10³

Using a³-b³=(a – b)(a² + ab + b²), we get

(b-10)(b²+10b+100)

Therefore, the factorization of the polynomial b³-1000 is (b-10)(b²+10b+100).

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Based on the data, m∠ABC = 113°, m∠DBC = 35°, and m∠ABD = 74°.

To find the value of these angles we must perform the following operations:

1. In the first point, to find the angle of ABC, we must take into account the values of ABD and DBC. In this case, to find ABC, we must add the values of ABD and DBC:

70° + 43° = 113°

2. In the second point, to find the angle of DBC we must subtract the values of EBC and EBC:

55° - 20° = 35°

3. In the third point, to find the angle of ABD we must subtract the values of ABC and DBC.

110° - 36° = 74°

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The number of miles of DNA we eat in a single meal is 500 million / 5,280 = 94,696.97 miles i.e

95,000 miles.

If there are approximately 10 feet of DNA in a single plant cell, then 50 million plant cells contain 50 million x 10 feet = 500 million feet of DNA. To convert this to miles, we need to divide by the number of feet in a mile, which is 5,280.

The number of miles of DNA we eat in a single meal is 500 million / 5,280 = 94,696.97 miles (rounded to two decimal places). This means that in just one meal, we consume an enormous amount of DNA that, if stretched out, could span almost 95,000 miles!

While this might seem like a lot, the DNA we consume is broken down during digestion and does not remain intact in our bodies. The human body contains trillions of cells, each with their own DNA, so the amount of DNA we consume from plants is relatively small in comparison.

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The measure of the three missing angles in the given rhombus are:

x = 122°

z = 58°

y = 122°

A rhombus is a quadrilateral with four interior angles. In a rhombus, the opposite angles are congruent while the adjacent angles are supplementary to each other.

x and 58° are adjacent angles and are therefore supplementary.

x = 180 - 58 = 122°

z = 58° (opposite angles)

y = x = 122° (opposite angles)

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After solving the given expression → F = - m + B/q³  for  [B], we get -

B = q³(F + M).

We have the following equation -

F = - m + B/q³

We have the following equation -

F = - m + B/q³

On solving for [B], we get -

F + M = B/q³

B = q³(F + M)

Therefore, the given expression after solving for [B], we get -

B = q³(F + M).

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Answer:

15 ft 45 ft 30 ft 60 ft

Step-by-step explanation:

Answer:

Angle NOR is also 129 im pretty sure,

Step-by-step explanation:

NOR and SRO are equivalent.

Answer: chst m3 ill help will more

Step-by-step explanation:

The equation ||αu v||^2 = α^2 ||u||^2 ||v||^2 does not hold in general.

Therefore the answer is False.

The left side of the equation is the square of the Euclidean norm of the product of a scalar and two vectors, which is ||αu v||^2 = (αu)^T (αu) = α^2 u^T u v^T v = α^2 ||u||^2 ||v||^2. The Euclidean norm, also known as the L2 norm, is a measure of the magnitude of a vector in a multi-dimensional space. It is defined as the square root of the sum of the squares of the vector's components.

The right side of the equation is the product of the squares of the norms of two vectors, which is not equal to the square of the norm of their product in general.

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See attachment for the graph of the reflection of f(x) across the y-axis

The function is given as:

f(x) = 1.5(0.5)^x

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have the following equation

f'(x) = 1.5(0.5)^-x

Rewrite the function as

g(x) = 1.5(0.5)^-x

So, we plot the graph of the function g(x)

See attachment for the graph of the reflection of f(x)

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step 1 :

g(x) = 1.5

step 2 :

g(0): 1.5

step 3 :

plot at (0,1.5)

step 4 :

g(1) = 3

g(-1) = .75

step 5 :

plot (1,3) & (-1,0.75)

step 6:

y=0

Dispersion is a measure of how spread out a set of data values is. For the given data, I'll calculate three common measures of dispersion: range, variance, and standard deviation.

Sorted data: 0, 0, 1, 1, 3, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 13, 14, 14, 15, 17, 18, 19, 20

1. Range: The range is the difference between the highest and lowest values in the dataset. In this case, the range is 20 (highest value) - 0 (lowest value) = 20.

2. Variance: Variance is the average of the squared differences between each data point and the mean of the dataset. First, calculate the mean (sum of values / number of values) which is 233/25 = 9.32. Next, find the squared differences between each data point and the mean, and then average these squared differences. The variance for this dataset is approximately 34.93.

3. Standard Deviation: The standard deviation is the square root of the variance. In this case, the standard deviation is approximately √34.93 ≈ 5.91.

In summary, the range for the given data is 20, the variance is approximately 34.93, and the standard deviation is approximately 5.91. These measures of dispersion provide insights into the variability of the data.

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Answer:

If its per month then its 900

Step-by-step explanation:

3600/4 = 900

900*4 = 3600

We are given the polynomial

Find the roots:

To find the roots of this polynomial, we want to solve the following equation

On the left side, we can factor the polynomial as follows

This leads to the following two equations

with solution x=0, and the equation

by subtracting -2 from both sides , we get

Finally, by dividing both sides by -7, we get

So, the roots of this polynomial are x=0 and x=2/7.

Describe the end behavior:

To describe the end behavior of a polynomial we should first see how the polynomial is written

In here, we see that we have a power of 4 and a power of 3. Consider that the power of 4, as x grows bigger and bigger (or smaller and smaller) the power of 4 will dominate the behavior of the polynomial as x⁴ grow bigger and bigger than x³. So, we can forget the other part and focus on the polynomial

Note that as x is a positive number, then x^4 is also a positive number. So as x grows bigger and bigger, we would get a more negative number, since we are multiplying -7 (a negative number) with a really big positive number (x^4). Then this polynomial will go to - infinity as x grows bigger and bigger.

Also, to understand the end behaviour, we should see how the polynomial behaves as x becomes a really negative number. As before, we can only focus on the polynomial

note that if x is a negative number, x^4 is again a positive number. So, as x becomes more negative (approaching - infinity) the number -7x^4 would once again be a negative number. So, the end behavior as x goes - infinity is also - infinity.

Sketch:

For the sketching, we will use a sketchin software, so the polynomial would look like this

Answer:

a is 17 1/2 i dont know b sorry

Answer:

A.7/2

alternate form: 3 1/2

B.36/7

alternate form: 5 1/7

i hope it help

Answer:

yes.

Step-by-step explanation:

The interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.

The answer to this question is option D, which is μ - σ to Q3. To understand why this is the correct answer, we need to first understand what each of the intervals represents. Q1 and Q3 are the first and third quartiles of the data set, respectively. μ is the mean of the data set, and σ is the standard deviation.

When we look at the interval μ - σ to Q3, we can see that it includes the upper quartile and some of the data points to the left of it. This means that the area under the normal curve within this interval will be relatively small compared to the other options.

On the other hand, option B includes the mean and a larger range of data points, which would result in a larger area under the curve. Option C includes Q1 and a larger range of data points, which would also result in a larger area. Option A includes both Q1 and Q3, which cover the majority of the data set and would therefore have the largest area under the curve.

In summary, the interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.
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Answer:

the slope is 2

Step-by-step explanation:

it goes up 2 and over 1 tiles

Check the picture below.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the Moonbeam Drive

\((\stackrel{x_1}{15}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{20}-\underset{x_1}{15}}} \implies \cfrac{-4}{5}\)

that means that the slope of Comet Parkway will be

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-4}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-4}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-4}\implies \cfrac{5}{4}}}\)

so we're really looking for the equation of a line whose slope is 5/4 and that it passes through (2 , 6)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{4}}(x-\stackrel{x_1}{2}) \\\\\\ y-6=\cfrac{5}{4}x-\cfrac{5}{2}\implies y=\cfrac{5}{4}x-\cfrac{5}{2}+6\implies {\LARGE \begin{array}{llll} y=\cfrac{5}{4}x+\cfrac{7}{2} \end{array}}\)

From law of cosine formula, the width of lake for which Julia wants to determine the distance at certain points across a lake is equals to the 4023.4 meters.

Law of cosine in triangle is used to determine the length of third side of triangle when two other sides and angle between them is known. Cosine formula is c² = a² + b² - 2ab cosC , where

Julia wants to determine the distance at certain points across a lake. See the above figure and reconigse the measurements. Here, the width of lake is represented by AB. There is formed a triangle ABC, with following details,

Length of side AC = 2.82 mi

Length of side BC = 3.86 mi

Measure of angle C = 40.3°

We have to determine value of AB. Using the law cosine formula, AB² = BC² + AC² - 2AC× BC cosC

=> AB² = 2.82² + 3.86² - 2×2.82×3.86 ×cos( 40.3°)

=> AB² = 7.9524 + 14.8696 - 21.7764 ×cos( 40.3°)

=> AB² = 22.852 - 16.603

=> AB ² = 6.2485

=> AB = 2.4996

Hence, required width is 2.5 miles. But we needs answer in meter then convert miles into meters, 1 mile = 1609.344 m

so, 2.5 miles = 2.5 × 1609.344 meters = 4023.36 m ~ 4023.4 meters.

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Complete question:

The above figure complete the question.

julia needs to determine the distance at certain points across a lake. her crew and she are able to measure the distances shown on the diagram below. find how wide the lake is to the nearest tenth of a meter.