Which of the following
represents this line graph?
Enter a, b, c, or d.
5
a. 3x - 5 > 10
b. 3x - 5 < 10
c. - ≤ x ≤ 5
d.≥ x ≥5
5/3

Answer:

52 Labels

8 cabinets with 5 drawers 8x5=40

3 cabinets with 4 drawers 3x4=12

40+12=52

Answer:

Heather will need to make 57 labels to complete the task.

Step-by-step explanation:

There are 12 file cabinets.

Three of them have 4 drawers.

Heather will need to make 3*4=12 labels for these cabinets

The rest of the cabinets (12-3=9) have 5 drawers.

Heather will need to make 9*5=45 labels for these cabinets

The total of labels needed is 12+45=57.

Heather will need to make 57 labels to complete the task.

 By multiplying matrices B and A, we obtain the product BA. Using BA, we can solve the system of equations y + 2z = 7, x - y = 3, and 2x + 3y + 4z = 17.the values of x, y, and z are -1, 2, and 1 respectively

To find the product BA, we multiply matrix B with matrix A. The resulting matrix will have the same number of rows as B and the same number of columns as A. The product BA will be used to solve the given system of equations.
The product BA can be computed by multiplying each row of matrix B by each column of matrix A and summing the results. The resulting matrix will be:
Now, we can use the product BA to solve the system of equations:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.

1 -1 2
2 3 1
0 4 2
We can rewrite this system of equations as:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.
By comparing the coefficients of x, y, and z in the system of equations with the entries in the matrix BA, we can determine the values of x, y, and z.
Solving the system of equations using matrix BA, we get:
x = -1,
y = 2,
z = 1.
Therefore, the values of x, y, and z are -1, 2, and 1 respectively.

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The complete question is:
Given A=
⎣2 2 -4|
|-4 2 -4|
|2 -1 5|
, B=
⎣1 -1 0|
⎢2 3 4|
⎢0 1 2|
, find BA and use this to solve the system of equations y+2z=7, x−y=3, 2x+3y+4z=17.

The curve is smooth for \(t\neq 0\) on the intervals (-∞, 0), (0, ∞)

We have to consider the curve

                                               \(r(t) = 8t^{2}i + 7t^{3}j\)

Now, the objective is to find the open intervals when on which the curve given by the vector valued function is smooth, using the result.

The parametrization of the curve represented by the vector valued function

                                       \(r(t) = f(t)i + g(t)j + h(t)k\)

This equation is smooth on an open interval when f'(t), g'(t), and h'(t) are continuous on \(l\) and r'(t) \(\neq\) 0 for any value of t in the interval.

Now, we know the vector equation:

\(r(t) = 8t^{2}i + 7t^{3}j\)

Differentiating r(t) with respect to r,

\(r'(t) = 16t i + 21t^{2} j\)

At t = 0, equate r'(t) = 0.

\(r'(0) = 16(0) + 21(0)^{2}\)

Therefore, the curve is smooth for all values except 0, as we can see above.

Hence, the curve is smooth for \(t\neq 0\) on the intervals (-∞, 0), (0, ∞).

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The researchers would need to include at least 278 encounters in their sample to ensure that the standard deviation of the sample proportion is no larger than 0.03.

To determine the required sample size, we need to use the formula for the standard deviation of the sample proportion (σp):

\(\sigma_p = \sqrt{(p * (1 - p) / n)}\)

where:

p is the estimated proportion (we don't have this information, so we'll use 0.5 as a conservative estimate for maximum variance),

n is the sample size.

Since the researchers want to ensure that the standard deviation of the sample proportion is no larger than 0.03, we can set up the following inequality:

0.03 ≥ √(0.5 * (1 - 0.5) / n)

Squaring both sides of the inequality to eliminate the square root:

0.03² ≥ 0.5 * (1 - 0.5) / n

0.0009 ≥ 0.25 / n

Now, solve for n:

n ≥ 0.25 / 0.0009

n ≥ 277.78

Since the sample size (n) must be a whole number, the researchers would need to include at least 278 encounters in their sample to ensure that the standard deviation of the sample proportion is no larger than 0.03. Rounding up, the required sample size is 278 encounters.

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Answer:

11 servings include 11(3/5), or 33/5, or 6 3/5, cups of rice.

Step-by-step explanation:

If 1 serving includes 3/5 cup of rice, then multiplying both numerals here by 11 produces a similar statement for 11 servings:

11 servings include 11(3/5), or 33/5, or 6 3/5, cups of rice.

Answer:

86400 seconds

Step-by-step explanation:

The unit of measurement "day" (symbol d) is defined as 86,400 SI seconds.

Answer:

86,400

Step-by-step explanation:

Answer:

Step-by-step explanation:

Between 1849 and 1852, the population of California more than doubled due to the California Gold Rush.

Between 1849 and 1852, the population of California more than doubled. California saw a population boom in the mid-1800s due to the California Gold Rush, which began in 1848. Thousands of people flocked to California in search of gold, which led to a population boom in the state.What was the California Gold Rush?The California Gold Rush was a period of mass migration to California between 1848 and 1855 in search of gold. The gold discovery at Sutter's Mill in January 1848 sparked a gold rush that drew thousands of people from all over the world to California. People from all walks of life, including farmers, merchants, and even criminals, traveled to California in hopes of striking it rich. The Gold Rush led to the growth of California's economy and population, and it played a significant role in shaping the state's history.

The final answer is 8013.996 with 6 significant figures. In scientific notation, the answer is 8.013996 × 10³.

a) 7987.34 + 23.456 - 7.8

1. Addition: 7987.34 + 23.456 = 8020.796

The number of significant figures in 8020.796 is 6, which is the same as the number of significant figures in 7987.34 (the number with the least significant figures).

2. Subtraction: 8020.796 - 7.8 = 8013.996

The number of significant figures in 8013.996 is 6, which is the same as the number of significant figures in 8020.796 (the number with the least significant figures).

Hence, the final answer is 8013.996 with 6 significant figures. In scientific notation, the answer is 8.013996 × 10³.

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Answer:

62.5 miles per hour

Step-by-step explanation:

Given data

distance= 125m

time= 2 hours

We know that

speed= distance/time

Subsitute

Speed= 125/2

speed= 62.5 miles per hour

The vector field F = (7x + 3y, 3x + 5y) is not conservative. To evaluate the line integral of F.dr along the curve C: F(t) = (t+7, t+3j), for 0 < t < 3, we can use the parameterization of the curve and calculate the integral. The line integral involves integrating the dot product of F and the tangent vector dr along the curve C to find the total work done by the vector field F.

A vector field F is said to be conservative if it can be expressed as the gradient of a scalar function, i.e., F = ∇f, where f is a scalar potential function. To determine if F = (7x + 3y, 3x + 5y) is conservative, we can check if the components satisfy the condition ∂F₁/∂y = ∂F₂/∂x.

In this case, we have ∂F₁/∂y = 3 and ∂F₂/∂x = 3, indicating that the vector field F does not satisfy the conservative condition.

To evaluate the line integral of F.dr along the curve C: F(t) = (t+7, t+3j), for 0 < t < 3, we can parameterize the curve as r(t) = (t, t) and compute the integral ∫C F.dr = ∫(0 to 3) [(7t+3t)dt + (3t+5t)dt]. This involves integrating the dot product of F and the tangent vector dr along the curve C.

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Answer:

So the slope is -5/2.

Step-by-step explanation:

Answer:

1a. 5x+14

1b. 5x+14 < 65

1c. x=51/5

Step-by-step explanation:

Problem 1

PMT = 505.76 = monthly payment

k = monthly interest rate in decimal form

k = 0.043/12 = 0.003583333 (approximate)

n = 5*12 = 60 months

PVOA = present value of ordinary annuity

PVOA = PMT * ( 1 - (1+k)^(-n) )/k

PVOA = 505.76 * ( 1 - (1+0.003583333)^(-60) )/0.003583333

PVOA = 27,261.436358296

When rounding to the nearest dollar, we get $27,261

Your teacher made a mistake in choosing the formula. S/he mixed up present value ordinary annuity with annuity due. The (1+k) portion at the end is ignored. I rewrote the 1/( (1+k)^n ) sub-portion as (1+k)^(-n) to avoid a bit of clutter.

--------

To type this into excel we will write

=PV(0.043/12,5*12,505.76,0,0)

That will produce the result of -27,261.44. The negative is to indicate a cash outflow.

Don't forget about the equal sign up front when writing excel formulas.

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

Problem 2

L = loan amount = 23099

k = interest rate per month = 0.051/12 = 0.00425 exactly

n = number of months = 5*12 = 60 months

PMT = monthly payment

PMT = (Lk)/(1 - (1 + k)^(-n) )

This formula is the result of solving PVOA = PMT * ( 1 - (1+k)^(-n) )/k for "PMT". The PVOA value is the loan amount in this case.

Let's plug in the values mentioned

PMT = (Lk)/(1 - (1 + k)^(-n) )

PMT = (23099*0.00425)/(1 - (1 + 0.00425)^(-60) )

PMT = 436.965684557303

PMT = 437 when rounding to the nearest whole number

--------

To do this in excel, we type in

=PMT(0.051/12,5*12,23099,0,0)

The output should be -436.97 which rounds to -437.

The value is negative to represent a cash outflow, but your teacher mentions to post the answer as a positive value.

The dimensions of the provided rectangle's sides ST and PT are 4 and 4√3 units, respectively.

Given: PFST is a rectangle with a radius of four and angle SOT of 60 degrees.

We must locate ST and PT.

We will thus apply the idea of cosine of an angle to find the same.

The law of cosine is expressed as follows for a triangle with sides α, β, and γ with angles, and:

\(\mathrm {b^2=a^2+c^2-2ac\cdot \cos \left(\beta \right)}\)

Since the radius of the circle O is made up of the points OS, OP, OF, and OT, their measurements are all equal.

Now, considering the Δ SOT for ST.

We have,

β = 60° and a and c = 4.

Applying the law:

\(\mathrm b=\sqrt{4^2+4^2-2\cdot \:4\cdot \:4\cos \left(60^{\circ \:}\right)}\)

Solving we get,

b = 4

Therefore, ST = 4 units.

Similarly, considering the Δ POT for PT.

Here, ∠POT = 180° - 60° [linear pair]

∠POT = 120°

So, we have,

β = 120° and a and c = 4.

Applying the law:

\(\mathrm b=\sqrt{4^2+4^2-2\cdot \:4\cdot \:4\cos \left(120^{\circ \:}\right)}\)

Solving we get,

b = 4√3 units

Therefore, PT = 4√3 units.

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The figure is given below:

Answer:

Step-by-step explanation:

Let the initial percentage to be 30%

If it started to loose 2.5% every hour where;

t represents the time after Charlotte left her house

The amount of percent remaining every hour will form an arithmetic sequence as shown;

30, (30-2.5), (30-5.0),...

30, 27.5, 25.0...

Using the nth term for calculating an arithmetic sequence

B = a + (t-1)d

a is the first term = 30

d is the common difference = 27.5-30 = 25-27.5 = -2.5

t is the time

Substitute the given values into the formula;

B = 30 + (t-1)(-2.5)

B = 30+(-2.5t+2.5)

B = 30-2.5t+2.5

B = 32.5 - 2.5t

Hence equation for B, in  terms of t, representing the charge remaining in Charlotte's battery, as a percentage,  t hours after Charlotte left her house is B = 32.5 - 2.5t

The inverse of f(x) will be a relation if the original function's graph contains any location where a horizontal line would cross itself twice, but the inverse of that function won't be a function in and of itself.

Does a function's inverse always represent a relationship?

Essentially, obtaining an inverse is only a matter of changing the x and y coordinates. Although it might not always be a function, this newly generated inverse will be a relation. Sometimes a function's inverse isn't actually a function!

The inverse will also be a function if all horizontal lines only ever intersect one place on the original graph.

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Answer:

321.68feet

Step-by-step explanation:

Given the following

Top of the house above the sea level  = 150feet = opposite

Angle of elevation = 25°

Required

Distance from the boat to the base of the house(adjacent)

Using the SOH CAH TOA identity

tan theta = opp/adj

tan 25 = 150/d

d = 150/tan25

d = 150/0.4663

d = 321.68

Hence the required distance is  321.68feet

Answer:

h (1,2), w (3,4), y (6,0)

Step-by-step explanation:

Reflecting across y-axis means only changing the x -value between negative and positive. Flipping the sign

Answer:

\(\frac{-1}{81x^4y^16}\)

Step-by-step explanation:

→Rewrite the expression so that the exponent is no longer negative. To do this, you write it as:

\(\frac{-1}{(3xy^4)^4}\)

→Apply the exponent (4) to the 3, x, and \(y^4\):

\(\frac{-1}{81x^4y^16}\)

The solution is: red<yellow<green<blue<violet are the colors.

The light spectrum contains waves with specific wavelength which can be classified into groups. Most of the groups are invisible to the eye (like infrared, microwaves, radio waves, gamma rays, etc.) however, there is one group that is known as visible light.

Visible light allows us to see colors from red all the way to violet. The colors have different frequencies and wavelengths. The wave with the highest frequency also has the highest energy (which in this case is violet). Hence, as the frequency decreases, the energy will also decrease, making violet have the highest energy, and red have the lowest energy.

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complete question:

which answer has the colors in order from the lowest energy to the highest? group of answer choices red, blue, green blue, red, green blue, green, red red, green, blue

Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

For given question,

A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.

so, the probability that someone have this belief is P = 0.85

We know that in probability,

p = 1 - q

where;

p is probability of success

q is probability of failure.

Thus the probability that someone does not have this​ belief would be,

= 1 - P

= 1 - 0.85

= 0.15

Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

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Answer: 40°

Step-by-step explanation:

First angle can be represented as x, second angle can be represented as y, and the third angle can be represented as z.

x + y + z = 180°

Since the first and second angles are equal, x = y, we can replace y with x.

x + x + z = 180°

The third angle is 2.5 times the first, which can be written as 2.5x.

x + x + 2.5x = 180 (now we solve for x)

4.5x = 180

x = 40°

Check:

40 + 40 + 40(2.5) = 180°

180°=180°

$1.54/1 notebook

First you set up the proportion 3/$4.62 = 1/$x (x is unknown)

Then you divide $4.62 by three to find the price of 1 notebook. I used the bowtie method, there is other ways, but I find it the easiest

The intermediate step in the from (x+a)²=b for the equation -5x²+40x=320 is (x-4)²=80

We should know that a quadratic equation is the equation whose highest power of the variable is 2

The given parameter is

(x+a)²=b

in completing the square of the equation,-5x²+40x=-320

rewrite the equation to have

5x²-40x--320=0

Divide through by 5 to have

x²-8x-64=0

x²-8x=64

make the left hand side a perfect square

x²-8x+16=64+16

factorize the LHS to have

x²-4x-4x+16=80

(x²-4x)-(4x+16)=80

(x-4)²=80

Therefore the intermediate step is (x-4)²=80

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Answer:

170.16 ft

Step-by-step explanation:

tan10° = 30/x

x = 30x/ tan 10° = 30/0.1763

=170.16 ft

The average velocity between 3 and 6 seconds will be found with the following equation:

They will be exactly 124 miles apart 40 minutes before they meet.

First, we can find the combined speed of Car A and Car B by adding their individual speeds:

68 mph + 76 mph = 144 mph

This means that they will be covering a total distance of 144 miles every hour.

To find out how far apart they will be after 40 minutes, we need to calculate how much distance they will cover in that time.

We know that 60 minutes = 1 hour, so 40 minutes = 40/60 = 2/3 hour.

So, in 40 minutes, Car A will cover a distance of:

68 mph × 2/3 hour = 45.33 miles

And Car B will cover a distance of:

76 mph × 2/3 hour = 50.67 miles

Therefore, the total distance they will cover together in 40 minutes is:

45.33 miles + 50.67 miles = 96 miles

Subtracting this distance from their initial distance of 220 miles, we get:

220 miles - 96 miles = 124 miles

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Answer:

log base 4 (5x + 4) = 3

Step-by-step explanation:

a^b=c  is  loga(c)=b

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Therefore, the pool is filling up at a rate of 10 gallons per minute.

a. In this scenario, the independent variable is time (measured in minutes), and the dependent variable is the amount of water in the pool (measured in gallons).

b. The unit rate of change is the rate at which the dependent variable (amount of water in the pool) changes per unit of the independent variable (time). In this case, the unit rate of change is 10 gallons per minute, which means that the pool is filling up at a rate of 10 gallons per minute.

To calculate the unit rate of change step by step, you can follow these steps:

Determine the change in the dependent variable (amount of water in the pool) over a specific interval of time. For example, if you want to calculate the unit rate of change for the first minute, the change in the dependent variable would be 10 gallons (since the hose is filling the pool at a rate of 10 gallons per minute).

Determine the change in the independent variable (time) over the same interval of time. In this case, the change in the independent variable would be 1 minute.

Divide the change in the dependent variable by the change in the independent variable to get the unit rate of change. In this case, the unit rate of change would be:

Unit Rate of Change = Change in dependent variable / Change in independent variable

= 10 gallons / 1 minute

= 10 gallons per minute

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