If you have a system of two equations with two unknowns, and the graphs of
the two equations do not intersect, the system must have
A. at least 1 solution
B. exactly 1 solution.
C. no solution
D. more than 1 solution

Answer:

D

Step-by-step explanation:

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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The total cash due at signing is $3800.

Option A is the correct answer.

We have,

The total cash due at signing is the sum of the down payment, security deposit, acquisition fee, and the first month's lease payment.

So,

Down payment = $2500

Security deposit = $375

Acquisition fee = $500

First month's lease payment = $425

The total cash due at signing is:

= $2500 + $375 + $500 + $425

= $3800

Thus,

The total cash due at signing is $3800.

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3.6 years will have passed when 115 grams of thorium 234 is left.

(a) To find the amount of thorium 234 left after 0.5 years, we can substitute t = 0.5 and A0 = 1000 into the given equation and solve for At:

[tex]A_t = A0e^{(-10.498t)}\\\\A_t = 1000e^{(-10.498(0.5))}\\\\A_t = 679.6\ grams[/tex]

Therefore, approximately 679.6 grams of thorium 234 will be left after 0.5 years.

(b) To find when 115 grams of thorium 234 will be left, we can set At = 115 in the given equation and solve for t:

[tex]A_t = A_0e^{-10.498t}\\\\115 = 1000e^{-10.498t}\\\\ln(115/1000) = -10.498t\\\\t = 3.6\ years[/tex]

Therefore, approximately 3.6 years will have passed when 115 grams of thorium 234 is left.

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(a) The distribution of X is X ~ N(151, 24)

(b) The probability that the average price is between $152 and $155 is 0.950

(c) The quartile for the average textbook price for this sample size is $167.2

(d) The assumption of normal distribution is necessary

Given that

Mean = 151

Standard deviation = 24

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(151, 24)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (152 - 151)/24 and z = (155 - 151)/24

Evaluate

z = 0.042 and z = 0.167

So, we have

P = P(0.042 < z < 0.167)

Evaluate

P = 0.95044

Approximate

P = 0.950

This is calculated as

Q₃ = Mean + 0.675 * Standard deviation

So, we have

Q₃ = 151 + 0.675 * 24

Evaluate

Q₃ = 167.2

Hence, the quartile for the average textbook price for this sample size is $167.2

Yes, the assumption is necessary

This is because

The distribution has a sample size greater than 25 as required by the central limit theorem

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Answer:

7c1 is an algebraic expression that evaluates to 47. The expression is made up of two terms, 7 and c1. The letter c is a variable and the number 1 represents the exponent of the variable. Therefore, 7 multiplied by the c to the power of 1 is equal to 7 times c, which is equal to 47.

6p4 is an algebraic expression that evaluates to 6,040. The expression is made up of two terms, 6 and p4. The letter p is a variable and the number 4 represents the exponent of the variable. Therefore, 6 multiplied by the p to the power of 4 is equal to 6 times p to the fourth power, which is equal to 6,040.

Answer:

[tex]h(x) = 2 {x}^{2} + 5x - 3[/tex]

[tex]h(x) = (2x - 1)(x + 3)[/tex]

-The component functions must both be linear.

-The component functions must have y-intercepts with different signs.

The surface area of the cylinder is 603.19 square meters

From the question, we have the following parameters that can be used in our computation:

Radius, r = 8 meters

Height, h = 4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 8 * (8 + 4)

Evaluate

Surface area = 603.19

Hence, the surface area is 603.19 square meters

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The value of sin(θ - φ) = sin(A - B) in simplest form is sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800

Use the trigonometric identity sin(α - β) = sin α cos β - cos α sin β to find sin(θ - φ), where θ = A and φ = B.

First, find cos A and sin B using the given information:

Since sin A = 53/45, use the Pythagorean identity cos² A + sin² A = 1 to find cos A:

cos² A + (53/45)² = 1

cos² A = 1 - (53/45)²

cos A = ± √(1 - (53/45)²)

Since A is a positive acute angle, take the positive square root:

cos A = √(1 - (53/45)²)

Similarly, since cos B = 29/20, use the Pythagorean identity cos² B + sin² B = 1 to find sin B:

sin² B = 1 - cos² B

sin B = ± √(1 - cos² B)

Since B is a positive acute angle, take the positive square root:

sin B = √(1 - (29/20)²)

Use the identity sin(α - β) = sin α cos β - cos α sin β to find sin(A - B):

sin(A - B) = sin A cos B - cos A sin B

= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)

Simplifying this expression:

sin(A - B) = (53/60) - √(2561)/900

Finally, use the identity sin(θ - φ) = sin θ cos φ - cos θ sin φ to find sin(θ - φ) = sin(A - B):

sin(A - B) = sin θ cos φ - cos θ sin φ

= sin A cos B - cos A sin B

= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)

= (53/60) - √(2561)/900

Therefore, the value of sin(θ - φ) = sin(A - B) in simplest form is:

sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800

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The required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.

The distance traveled by Zeek is:

84,240,000,000,000 miles away / 2.5 = 33,696,000,000,000 miles away

We can write this in scientific notation as:

3.3696 × 10¹³ miles

Thus, the required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.

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A hot dog costs 2.25 we get it by solving the equation

Let's denote the cost of one hot dog by x.

Then we can set up two equations:

5x + 6y = 18.39

x + 2y = 4.63

where y is the cost of one bag of chips.

We want to solve for x.

Let us isolate variable y in the second equation

y = 4.63 - x/2

Substitute the y equation in the equation (1)

[tex]$5x + 6\left(\frac{4.63 - x}{2}\right) = 18.39$[/tex]

Simplifying this equation gives:

5x + 13.89 - 3x = 18.39

2x = 4.5

x = 2.25

Hence, a hot dog costs 2.25.

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The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄

There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.

Now, we are given the fraction as an improper fraction in the form of 2³₄.

Rewriting as a whole number and a fraction gives:

2 + ³/₄

Breaking down the whole number into a fraction is done as:

1 + 1 + ³/₄

= ⁴/₄ + ⁴/₄ + ³/₄

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The monthly cost for 56 minutes of calls is given as follows:

$18.05.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

For 38 minutes of call, the price increases by $4.94, hence the slope of the linear function, representing the cost per minute, is given as follows:

m = 4.94/38

m = 0.13.

56 minutes is 30 minutes less than 86 minutes, hence the cost is given as follows:

C(56) = 21.95 - 30 x 0.13

C(56) = $18.05.

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Answer:

The area is 44

Step-by-step explanation:

If you add the numbers that across from each other you would get 12+12+2+2+8+8= 44

ok, let's assume the rate is 0.075 per minute, if we convert that to percentage that'd be 0.075*100 or 7.5% per minute, so we can assume the bread is cooling off at 7.5% per minute after coming out of the oven at 340°F and we need it at 80°F so we can slice it and put some butter on it.

now, we can look at this from a Decay standpoint and say

we have a temperature of 340°F, decaying at 7.5% per minute, how long before it turns into 80°F?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 80\\ P=\textit{initial amount}\dotfill &340\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=minutes \end{cases}[/tex]

[tex]80 = 340(1 - 0.075)^{t}\implies \cfrac{80}{340}= 0.925^t\implies \cfrac{4}{17}=0.925^t \\\\\\ \log\left( \cfrac{4}{17} \right)=\log(0.925^t)\implies \log\left( \cfrac{4}{17} \right)=t\log(0.925) \\\\\\ \cfrac{ ~~ \log\left( \frac{4}{17} \right) ~~ }{\log(0.925)}=t\implies 18.56\approx t\qquad \textit{almost 19 minutes}[/tex]

The derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)

The given function is  f(x)=(3x²−4x+1)⁴

We have to find the derivative of the function

By using chain rule we find the derivative

f'(x)=4(3x²−4x+1)³ d/dx(3x²−4x+1)

=4(3x²−4x+1)³ (6x-4)

Hence, the derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)

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Answer: 98 deg

Step-by-step explanation:

angles 3 and 4 are supplementary; this means their sum is 180 degrees.

so simply put, 180 - angle 3 = angle 4

180 - 82 = 98

The total area that needs to be covered which is indicated by the shaded area would be =220ft²

To calculate the area that needs to be covered, the formula that should be used is the formula for the area of a rectangle which is given below as follows;

Area of rectangule =2( length×width)

where ;

length = 22ft

width = 5ft

area = 2× 22×5

= 220ft²

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There are 1440 minutes in a day (24 hours x 60 minutes = 1440 minutes).

To convert 4320 minutes to days, divide 4320 by 1440:

4320 ÷ 1440 = 3

Therefore, 4320 minutes is equivalent to 3 days.

Answer: 3 days

Step-by-step explanation:

About 71 members of the group are expected to be between 51 years old and 59 years old.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:

68%.

Out of 104 people, the number of people with ages in the range is given as follows:

0.68 x 104 = 71 people. (rounded to the nearest integer).

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The actual bridge deck measures 4,320 square feet in size.

First, we need to convert the scaled dimensions to actual dimensions. Since the scale is 60:1, we need to multiply the scaled dimensions by 60 to get the actual dimensions.

The scaled length of the bridge deck is 36 inches, so the actual length is:

36 inches x 60 = 2,160 inches

The scaled width of the bridge deck is 4 4/5, or 24/5, inches. So the actual width is:

24/5 inches x 60 = 288 inches

To find the area of the actual bridge deck in square feet, we need to convert the actual dimensions to feet and then multiply:

Actual length in feet = 2,160 inches ÷ 12 inches/foot = 180 feet

Actual width in feet = 288 inches ÷ 12 inches/foot = 24 feet

Area in square feet = Actual length x Actual width = 180 ft x 24 ft = 4,320 square feet

Therefore, the area of the actual bridge deck in square feet is 4,320 square feet.

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Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.

If Keenan earns 1 mile for every $8 he spends, then he would need to spend 8 times as much money to earn the same number of miles as he did before.

In other words, he would need to spend $8 to earn 1 mile instead of $1 to earn 1 mile under the old program.

To calculate the new amount of money Keenan needs to spend to earn the miles for his trip, we would need to multiply the old amount by 8.

For example, if under the old program, Keenan needed to spend $10,000 to earn 25,000 miles for his trip, under the new program he would need to spend:

$10,000 x 8 = $80,000

So under the new program, Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.

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Answer:

LN and NK

Step-by-step explanation:

A perpendicular bisector of a line segment divides the line segment into 2 equal halves.

Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.

The two equal halves are segment LN and segment NK.

Therefore, segment LN is congruent to segment NK.

Answer:

96π

Step-by-step explanation:

the shape is made up of a cylinder and a cone.

Volume of cylinder = π r ² h

= π (3)² (9)

= 81π.

Volume of cone = (1/3) X vertical height X π r ²

= (1/3) (5) π (3)²

= 15π

volume of composite solid = 81π + 15π = 96π

The piecewise linear equation is y = -0.556x - 2.444, -8 ≤ x ≤ 1, y = 1.333x - 4.333, 1 < x ≤ 4 and y = -0.667x - 3.667 4 < x ≤ 10

From the question, we have the following parameters that can be used in our computation:

X: -8, 1, 4, 10

Y: 2, -3, 1, -3

In the interval [-8, 1], we have

X: -8, 1

Y: 2, -3

A linear equation is represented as

y = mx + c

Using the points, we have

-8m + c = 2

m + c = -3

So, we have

m = -0.556

c = -2.444

So, we have

-0.556x - 2.444, -8 ≤ x ≤ 1

In the interval (1, 4], we have

X: 1, 4

Y: -3, 1

Using the points, we have

m + c = -3

4m + c = 1

So, we have

m = 1.333

c = -4.333

So, we have

1.333x - 4.333, 1 < x ≤ 4

In the interval (4, 10], we have

X: 4  10

Y: 1   -3

Using the points, we have

4m + c = 1

10m + c = -3

So, we have

m = -0.667

c = 3.667

So, we have

-0.667x - 3.667 4 < x ≤ 10

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Answer:

60 and 40

Step-by-step explanation:

a) To find the number of people who like both tea and coffee, we can use the formula:

Number of people who like both = Number of people who like tea + Number of people who like coffee - Number of people who like only teaPlugging in the given values, we get:

Number of people who like both = 50 + 30 - 20 = 60Therefore, there are 60 people who like both tea and coffee.

b) To find the number of people who like either of the drinks, we can add the number of people who like tea only, the number of people who like coffee only, and the number of people who like both tea and coffee. Mathematically,

Number of people who like either drink = Number of people who like tea only + Number of people who like coffee only + Number of people who like both tea and coffeePlugging in the given values, we get:

Number of people who like either drink = 20 + (30-60) + 50 = 40Therefore, there are 40 people who like either tea or coffee (or both).

Answer:

x-intercept = -7

y-intercept = 1

rate of change = 1.25

Step-by-step explanation:

X and Y intercept are pretty to find.

Rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

So for our case it will be [tex]\frac{-0.75-(-2)}{-8-(-9)}[/tex]

The answer will be 1.25

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)