which statement gives a unit rate? a. for every cup, trey's cat ate for 0.75 of a day. b. for every day, trey's cat ate 1.5 cups. c. for every cup, trey's cat ate for 1.5 days. d. for every day, trey's cat ate 0.75 of a cup.

9514 1404 393

Answer:

  (a)  x = (3 -ln(3))/5 ≈ 0.819722457734

  (b)  y = 10

Step-by-step explanation:

(a) Taking the natural log of both sides, we have ...

  2x +1 = ln(3) +4 -3x

  5x = ln(3) +3 . . . . . . . . add 3x-1

  x = (ln(3) +3)/5 ≈ 0.820

__

(b) Assuming "lg" means "log", the logarithm to base 10, we have ...

  log(y -6) +log(y +15) = 2

  (y -6)(y +15) = 100 . . . . . . . taking antilogs

  y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100

  (y -19)(y +10) = 0 . . . . . . . . factor

The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.

The solution is ...

  y = 10

__

When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...

  f(x) = e^(2x+1) -3e^(4-3x)

Answer:

Step-by-step explanation:

e^(2x + 1) = 3e^(4 - 3x)

e^(2x + 1) = e^3(4-  3x)

lne^ (2x + 1) =ln e^3(4-  3x)

2x + 1 = 3*(4 - 3x)

2x + 1 = 12 - 9x

11x + 1 = 12

11x = 12 - 1

11x = 11

x = 1

====================

I've never worked with binary logs but I'll give this my best shot. If someone comes along and gives you a different answer, use it.

lg(y-6) + lg(y + 15) = 2

lg (y - 6)(y + 15) = 2

inverse (y - 6)(y + 15) = 2^2

(y - 6)(y + 15) = 4

y^2 + 9y - 90 - 4 = 0

y^2 + 9y - 94 = 0

y = 6.19

y = -15,19

Answer:

x + 125 = 2250 OR x = 2250 - 125

Step-by-step explanation:

Where x is the amount of money you have in your savings account. To solve for x, you can subtract 125 from both sides:

x = 2250 - 125

x = 2125

Therefore, you have $2125 in your savings account.

Hope this helps :)

Answer:

x = 4

Step-by-step explanation:

Translate the word problem into an equation

\(\frac{80}{5x} = 4\)

Solve for x

1.) Multiply both sides by 5x

80 = 20x

2.) Divide both sides by 20

4 = x

Answer:

she has to give him 4 dollars each week for 11 weeks since he already has 7 dollars.

Step-by-step explanation:

4 x 11 = 44 +7 = 51 so now he had enough for a skateboard.

Answer:

34.16

Step-by-step explanation:

42.7

x 0.8

-------

34.16

Answer:

34.16

Step-by-step explanation:  

2 5

42.7

 x

0.8

 =  

43.16

Answer:

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the lengths of the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.

Step-by-step explanation:

Was definetly not copy and pasted from g.o.o.g.l.e. no siree

Answer:

8

Step-by-step explanation:

if a = -b, then -a = b.

plug that into the (b = -c) problem, and you get -a = -c, or a = c

if a and c ar equal, then and b = -c, b also equals -a.

the problem then becomes a - b +c, where a = 8, c = 8, and b = -8

a = -b -> 8 = -(-8)

b = -c -> -8 = -(8)

a = c -> 8 = 8

Answer:

\(m\widehat{VU}=120^{\circ}\)

Step-by-step explanation:

The angle \(\angle TUV\) forms arc \(\widehat{TV}\). The measure of this arc is twice the measure of angle \(\angle TUV\), since \(U\) is a point on the circle. Since \(\overline{TU}\) forms an arc \(\widehat{TU}\), we can set up the following equation:

\(\widehat{TV}+\widehat{VU}=\widehat{TU}\).

Since arc TU represents half of a circle and there are 360 degrees in a circle, we can substitute the following values and solve for the measure of arc VU:

\(\\2\cdot 30^{\circ}+\widehat{VU}=180^{\circ},\\60^{\circ}+\widehat{VU}=180^{\circ},\\m\widehat{VU}=\boxed{120^{\circ}}\)

Answer:

m=\(\frac{1}{4}\)

Step-by-step explanation:

Gladly!

To find the slope, we need to find the change between point a and point b

With the difference between x1 and x2 being 4, and the difference between y1 and y2 being 1, we get a fraction that looks like this,

\(\frac{1}{4}\)

This right here is the slope of the line. Hope this helps!

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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The question asks for the x and y components of a displacement of 43 miles at an angle of 271 degrees

To find the x and y components of a displacement given an angle, we can use trigonometry. The x component represents the horizontal displacement, while the y component represents the vertical displacement.

In this case, the magnitude of the displacement is given as 43 miles, and the angle is 271 degrees. To find the x component, we can use the cosine of the angle, which gives us the ratio of the adjacent side (x) to the hypotenuse (43 miles). Similarly, to find the y component, we can use the sine of the angle, which gives us the ratio of the opposite side (y) to the hypotenuse (43 miles).

Using trigonometric functions, we can calculate the x and y components as follows:

x component = 43 miles * cos(271 degrees)

y component = 43 miles * sin(271 degrees)

Evaluating these expressions will provide the specific values for the x and y components of the displacement.

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Answer:

usage patterns are a variable used in market segmentation.

Step-by-step explanation:

Usage patterns are a variable used in behavioral segmentation.

Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.

Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.

By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.

Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.

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Answer:

x = 9

Step-by-step explanation:

The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

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Answer:

29%

Step-by-step explanation:

There are 100 boxes. 29 of them are shaded in, so we can divide that by 100.

29/100=0.29

0.29 is equal to 29%

Jane travels 8 miles much farther than her trainer. The solution is obtained using arithmetic operations.

What are arithmetic operations?

By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions add, subtract, divide, and multiply additionally allow for the specification of arithmetic operations.

3. Using pythagoras theorem, we get the equation as D² = 12² + 16².

⇒D² = 144 + 256

⇒D² = 400

⇒D = √400

⇒D = 20

4. Jane has traveled 28 miles in total whereas her trainer has traveled 20 miles.

So, the difference is 28-20= 8 miles

Hence, Jane travels 8 miles much farther than her trainer.

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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The rate of 50 deaths per 1,000 births is known as the infant mortality rate.

What is infant mortality rate?

Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age. Infant mortality rate is an essential demographic statistic for assessing population health status and identifying health disparities among different groups of the population.

IMR reflects the underlying mortality rate of infants in a society, which can be influenced by several factors, including maternal health, access to healthcare, nutrition, and socio-economic factors.Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age.

The rate of 50 deaths per 1,000 births is known as the infant mortality rate. The infant mortality rate is considered one of the most critical indicators of a country's health status and is often used to compare the health status of different populations.

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Answer:

19 and 11

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

-12, -15, -18, -21,

Notice that we are subtracting 3 each time

-12 -3 =-15

-15 -3 = -18

So -21 -3 = -24

Answer:

I think that the answer is B.

Step-by-step explanation:

go on demos and put in the problem on the left side. and the dot should be on the number two. and in the picture you have^ . it has the same dot as demos.

Answer:

see explanation

Step-by-step explanation:

In a parallelogram

• opposite sides are congruent

• the diagonals bisect each other

Then

UT = 27 ( congruent to  RS )

ST = 18 ( congruent to RU )

VS = 7 ( congruent to UV )

VT = 15 ( half of RT )

Answer:

941.33 in^2.

Step-by-step explanation:

The area of a semicircle = 1/2 area of circle = 1/2 * 3.14 * radius^2.

The radius = 1/2 * 26 = 13 in.

Total area = area of square + area of semicirccle

= 26^2 + 1/2 * 3.14 * 13^2

= 676 + 265.33

= 941.33 in^2.

The value of 4.62 times 3.78 equals 17.4828.

We have to find  4.62 times 3.78 in standard algorithm

To multiply 4.62 by 3.78 using the standard algorithm, follow these steps:

 4.62

x 3.78

------

 27756  (multiply 8 by 2)

+184368  (multiply 7 by 2, then 8 by 6, and add to the previous result)

-------

 17.4828  (the final answer)

Hence, the value of 4.62 times 3.78 equals 17.4828.

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1. 16.6 milliliters of the 15.8 M NH3 solution should be diluted to make 1050 mL of 0.250 M NH3.

2. The concentration of the final solution will be approximately 0.587 M.

1. To determine how many milliliters of the 15.8 M NH3 solution should be diluted to make 1050 mL of 0.250 M NH3, we can use the dilution equation:

C₁V₁ = C₂V₂

Where:

C₁ = initial concentration of the stock solution (15.8 M)

V₁ = volume of the stock solution to be diluted (unknown)

C₂ = final concentration of the diluted solution (0.250 M)

V₂ = final volume of the diluted solution (1050 mL or 1.05 L)

Rearranging the equation to solve for V₁:

V₁ = (C₂V₂) / C₁

Substituting the given values:

V₁ = (0.250 M * 1.05 L) / 15.8 M

V₁ = 0.0166 L

Converting liters to milliliters:

V₁ = 0.0166 L * 1000 mL/L

V₁ ≈ 16.6 mL

Therefore, approximately 16.6 milliliters of the 15.8 M NH3 solution should be diluted to make 1050 mL of 0.250 M NH3.

2. To determine the concentration of the final solution when a 13.0 mL portion of the stock solution is diluted to a total volume of 0.350 L, we can again use the dilution equation:

C₁V₁ = C₂V₂

Where:

C₁ = initial concentration of the stock solution (15.8 M)

V₁ = volume of the stock solution used (13.0 mL or 0.013 L)

C₂ = final concentration of the diluted solution (unknown)

V₂ = final volume of the diluted solution (0.350 L)

Rearranging the equation to solve for C₂:

C₂ = (C₁V₁) / V₂

Substituting the given values:

C₂ = (15.8 M * 0.013 L) / 0.350 L

C₂ ≈ 0.587 M

Therefore, the concentration of the final solution will be approximately 0.587 M.

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When a distribution is bell shaped, the percentage of the data values which will fall within 1 standard deviation of the mean is= 68%  

What does standard deviation mean in plain English?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                          Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

According to empirical rule, which is also  known as three-sigma rule or 68-95-99.7 rule, it is a rule of statistics which says that all observed data will fall within three standard deviations of the mean or average for a normal distribution.

1.68% falls within first standard deviation .

2.95% falls within the first two standard deviations.

3.99.7% falls within the first three standard deviations.

Therefore,

When a distribution is bell shaped, the percentage of the data values which will fall within 1 standard deviation of the mean is= 68%  

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If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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Answer:

-1/12x

Step-by-step explanation:

Let total people at the picnic=x

People who chose apple= 1/3x

People who chose orange= 3/4x

People who chose each of the fruit= People who chose apple + People who chose orange

=1/3x + 3/4x

= 4x+9x / 12

=13/12x

People who chose each of the fruit= 13/12x

what fraction of the people chose both of them?

Fraction of the people who chose both fruits= Total people at the picnic - People who chose each of the fruit

=x - 13/12x

=12x- 13x /12

= -1/12 x