Answer:
1 yard = 3 ft
75 yards = 75 * 3
75*3 = 225
He ran 225 ft
If you need inches = 225*12
inches = 2700 inches
Answer:
225 feet
Step-by-step explanation:
3 feet equals 1 yard
? Feet equals 75 yards
75 times 3 equals 225 feet
the time needed to complete a final examination in a particular college course is normally distributed with a mean of
The probability of a student completing the final examination in less than 65 minutes is 13.45%.
The time it takes to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. This can be expressed mathematically as X~N(77, 12).
The probability of a student completing the final examination in less than 65 minutes can be calculated by using the Z-score formula:
Z = (x - μ) / σ
Where x = 65 minutes, μ = 77 minutes, and σ = 12 minutes.
Plugging these values into the formula, we get:
Z = (65 - 77) / 12 = -1.17
Using a Z-score table, we can find the probability of a student completing the final examination in less than 65 minutes, which is equal to 0.1345, or 13.45%. Therefore, the probability of a student completing the final examination in less than 65 minutes is 13.45%.
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Carlisle Transport had $4,520 cash at the beginning of the period. During the period, the firm collected $1,654 in receivables, paid $1,961 to supplier, had credit sales of $6,916, and incurred cash expenses of $500. What was the cash balance at the end of the period?
To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.
Starting cash balance: $4,520
Cash inflows: $1,654 (receivables collected)
Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)
Total cash inflows: $1,654
Total cash outflows: $1,961 + $500 = $2,461
To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:
Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows
Cash balance at the end of the period = $4,520 + $1,654 - $2,461
Cash balance at the end of the period = $4,520 - $807
Cash balance at the end of the period = $3,713
Therefore, the cash balance at the end of the period is $3,713.
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Triangles ABC and ADC are shown below. Paul claims that triangles ABC and ADC are congruent.
Based on the diagram, determine whether each statement below can be used to justify the claim. Select Yes or No for each statement.
.
.
.
.
Triangles ABC and ADC are congruent because the triangles satisfy the AAS triangle congruence criterion. (Yes or No)
Triangles ABC and ADC are congruent because the triangles satisfy the ASA triangle congruence criterion. (Yes or No)
Triangles ABC and ADC are congruent
because there is a rotation that will carry one triangle onto the other. (Yes or No)
Triangles ABC and ADC are congruent because there is a reflection that will carry one triangle onto the other. (Yes or No)
Triangles ABC and ADC are congruent because there is a translation that will carry one triangle onto the other (Yes or No)
Answer:
1 no
2 yes
3 no
4 yes
5 no
(((()))))
Triangles ABC and ADC are congruent based on the ASA congruence theorem, and by reflection, one triangle can be carried onto the other triangle, therefore:
Statement 1 is NOStatement 2 is YESStatement 3 is NOStatement 4 is YESStatement 5 is NORecall:
The diagram shows the congruence theorem that can prove that two triangles are congruent.Two triangles that are reflection of each other can also be said to be congruent triangles.Thus:
The image of both triangles given shows that they have two pairs of angles and an included side, which means that the ASA Congruence Theorem can be used to prove their congruency. Therefore,
Statement 1 is NOStatement 2 is YES.Also, the transformation that can justify that triangles ABC and ADC are congruent is reflection that will carry one triangle onto the other triangle.
Therefore,
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Determine the average rate of change in median age per year from 1930 to 1960
A. -0.5 years of age per year
B. 20 years of age per year
C. -0.05 years of age per year
D. +0.05 years of age per year
Answer:
It's C -0.05 years of age per year
Step-by-step explanation:
Skylar invested $330 in an account paying an interest rate of 3 and 3/4% compounded continuously. Montraie invested $330 in an account paying an interest rate of 4 and 3/8% compounded annually. After 18 years, how much more money would Montraie have in his account than Skylar, to the nearest dollar?
The formula for annually compounded interest is:A=P*(1+r)^tA = 330*(1+0.04375)^18A ≈ $814.14Montraie has $814.14-$675.70 = $138.44 more in his account than Skylar, to the nearest dollar.
The problem is related to compound interest and it involves calculating the difference in the amount of money accumulated by Skylar and Mantri e after 18 years,
given that Skylar invested $330 in an account with an interest rate of 3 and 3/4% compounded continuously and Mantri e invested $330 in an account with an interest rate of 4 and 3/8% compounded annually.Compound interest formula is:
A=P(1+r/n)^(n*t)where A is the amount of money accumulated after t years P is the principal or initial investment r is the annual interest raten is the number of times interest is compounded in a year t is the time in Years For Skylar:Initial Investment,
P = $330Interest Rate, r = 3 and 3/4 %, which can be written as 3.75% in decimal form Time, t = 18 years Since the interest is compounded continuously, the number of times compounded, n = ∞.
The formula for continuously compounded interest is:
A=P*e^(r*t)
where e is the mathematical constant ≈ 2.71828A = 330*e^(0.0375*18)A ≈ $675.70
For Montraie:
Initial Investment, P = $330Interest Rate, r = 4 and 3/8 %,
which can be written as 4.375% in decimal From Time, t = 18 years Since the interest is compounded annually, the number of times compounded, n = 1.
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A lamina has the shape of a triangle with vertices at (-7,0), (7,0), and (0,5). Its density is p= 7. A. What is the total mass? B. What is the moment about the x-axis? C. What is the moment about the y-axis? D. Where is the center of mass?
A lamina has the shape of a triangle with vertices at (-7,0), (7,0), and (0,5). Its density is p= 7
To solve this problem, we can use the formulas for the total mass, moments about the x-axis and y-axis, and the coordinates of the center of mass for a two-dimensional object.
A. Total Mass:
The total mass (M) can be calculated using the formula:
M = density * area
The area of the triangle can be calculated using the formula for the area of a triangle:
Area = 0.5 * base * height
Given that the base of the triangle is 14 units (distance between (-7, 0) and (7, 0)) and the height is 5 units (distance between (0, 0) and (0, 5)), we can calculate the area as follows:
Area = 0.5 * 14 * 5
= 35 square units
Now, we can calculate the total mass:
M = density * area
= 7 * 35
= 245 units of mass
Therefore, the total mass of the lamina is 245 units.
B. Moment about the x-axis:
The moment about the x-axis (Mx) can be calculated using the formula:
Mx = density * ∫(x * dA)
Since the density is constant throughout the lamina, we can calculate the moment as follows:
Mx = density * ∫(x * dA)
= density * ∫(x * dy)
To integrate, we need to express y in terms of x for the triangle. The equation of the line connecting (-7, 0) and (7, 0) is y = 0. The equation of the line connecting (-7, 0) and (0, 5) can be expressed as y = (5/7) * (x + 7).
The limits of integration for x are from -7 to 7. Substituting the equation for y into the integral, we have:
Mx = density * ∫[x * (5/7) * (x + 7)] dx
= density * (5/7) * ∫[(x^2 + 7x)] dx
= density * (5/7) * [(x^3/3) + (7x^2/2)] | from -7 to 7
Evaluating the expression at the limits, we get:
Mx = density * (5/7) * [(7^3/3 + 7^2/2) - ((-7)^3/3 + (-7)^2/2)]
= density * (5/7) * [686/3 + 49/2 - 686/3 - 49/2]
= 0
Therefore, the moment about the x-axis is 0.
C. Moment about the y-axis:
The moment about the y-axis (My) can be calculated using the formula:
My = density * ∫(y * dA)
Since the density is constant throughout the lamina, we can calculate the moment as follows:
My = density * ∫(y * dA)
= density * ∫(y * dx)
To integrate, we need to express x in terms of y for the triangle. The equation of the line connecting (-7, 0) and (0, 5) is x = (-7/5) * (y - 5). The equation of the line connecting (0, 5) and (7, 0) is x = (7/5) * y.
The limits of integration for y are from 0 to 5. Substituting the equations for x into the integral, we have:
My = density * ∫[y * ((-7/5) * (y - 5))] dy + density * ∫[y * ((7/5) * y)] dy
= density * ((-7/5) * ∫[(y^2 - 5y)] dy) + density * ((7/5) * ∫[(y^2)] dy)
= density * ((-7/5) * [(y^3/3 - (5y^2/2))] | from 0 to 5) + density * ((7/5) * [(y^3/3)] | from 0 to 5)
Evaluating the expression at the limits, we get:
My = density * ((-7/5) * [(5^3/3 - (5(5^2)/2))] + density * ((7/5) * [(5^3/3)])
= density * ((-7/5) * [(125/3 - (125/2))] + density * ((7/5) * [(125/3)])
= density * ((-7/5) * [-125/6] + density * ((7/5) * [125/3])
= density * (875/30 - 875/30)
= 0
Therefore, the moment about the y-axis is 0.
D. Center of Mass:
The coordinates of the center of mass (x_cm, y_cm) can be calculated using the formulas:
x_cm = (∫(x * dA)) / (total mass)
y_cm = (∫(y * dA)) / (total mass)
Since both moments about the x-axis and y-axis are 0, the center of mass coincides with the origin (0, 0).
In conclusion:
A. The total mass of the lamina is 245 units of mass.
B. The moment about the x-axis is 0.
C. The moment about the y-axis is 0.
D. The center of mass of the lamina is at the origin (0, 0).
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After surgery, a patient drinks 2ounces of clear liquids every 2 hours. How many ounces will the patient drink in 8 hours?
Answer:
8
Step-by-step explanation:
Hope it helps pl give brainliest! :D
x+4y+32
Terms:
Variable:
Constant:
Coefficients:
Answer:
Terms: x, 4y, 32
variables: x, y
constant: 32
coefficients: 4, 1
Step-by-step explanation:
Hope this helps!
A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke assemblies and 88% of the logic circuits are satisfactory. Assuming that defects in keystroke assemblies are independent of defects in logic circuits, find the probability that a finished calculator will be satisfactory. Group of answer choices
Answer:
0.7304
Step-by-step explanation:
According to the Question,
Given That, A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke assemblies and 88% of the logic circuits are satisfactory.We have,
P(keystroke satisfactory) =0.83 , P(logic satisfactory)= 0.88
Assuming that defects in keystroke assemblies are independent of defects in logic circuitsSince the events are independent. So, the probability that a finished calculator will be satisfactory
⇒ 0.83×0.88
⇒0.7304
In the circle below, stack A D with bar on top is a diameter and stack A B with left right arrow on top is tangent at A. Suppose m stack A D C with overparenthesis on top equals 224 degree.
Find the measures of m angle C A B and m angle C A D. Type your numerical answers (without units) in each blank.
m angle C A B =
64
degree
m angle C A D =
26
degree
A circle with a diameter labeled A D, chord A C. A line tangent to the circle at E and that goes through point B on the outside of the circle.
The measure of angle ∠CAB will be 68 degrees and the measure of angle ∠CAD will be 22 degrees.
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
In the circle below, stack AD with a bar on top is diameter and stack AB with a left-right arrow on top is tangent at A. Suppose m stack ADC with over parenthesis on top equals 224 degrees.
Then the measures of m angle ∠CAB and m angle ∠CAD will be
Then we have
We know that
mADC = mAD + mDC
224° = 180° + mDC
mDC = 44°
Then we know the theorem, A chord's degree in the centre is double that of the chord's degree at the perimeter. Then we have
2 ∠CAD = 44°
∠CAD = 22°
Then the angle ∠CAB and angle ∠CAD are complementary angles. Then we have
∠CAB + ∠CAD = 90°
∠CAB + 22° = 90°
∠CAB = 68°
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Question
Find the surface area of the prism
HELP
Answer: 56 in
Step-by-step explanation:
4x7x2=56
Answer:
56 in
Step-by-step explanation:
4*7*2
A triangular prism has base edges 3 cm, 6 cm, and 7 cm long. Its lateral area is 464 cm^2. What is the height of the prism? Simplify your answer.
Answer:
A triangular prism has base edges 4 cm, 5 cm, and 6 cm long. Its lateral area is
300 cm2.
What is the height of the prism?
1. You have 15 apples and 25 oranges. Write the ratio
for the number of apples to oranges.
2. Solve the proportion:
X 10
9
12
=
3. The scale factor for the blueprints for a room is 1 in.
to 12 ft. . If the back wall of the room has the dimension
of 8 in. on the blueprints, how long is the actual length
back wall?
Answer:
3/5 x = 7.5 96 ftStep-by-step explanation:
You want the solutions to various problems involving ratios, proportions, and scale factors.
1. RatioThe ratio of 15 apples ot 25 oranges can be written several ways, with and without units:
15 apples to 25 oranges, or 15 to 25.
Reduced to 3 apples to 25 oranges, or 3 to 5
15 apples : 25 oranges, or 15 : 25
Reduced to 3 apples : 5 oranges, or 3 : 5
15 apples / 25 oranges, or 15/25
Reduced to 3 apples / (5 oranges), or 3/5
2. Proportion
You can solve the proportion ...
x/9 = 10/12
by multiplying both sides by 9:
x = 9·10/12 = 90/12
x = 15/2 = 7.5
3. Scale factorIf each inch represents 12 ft, then 8 inches represents 8·12 ft = 96 ft.
The actual length of the back wall is 96 feet.
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Find the seventh term of the geometric sequence from the given information. Express the term as an integer or simplified fraction.
a2 = -7 and r = 1/2
The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term
To find the seventh term of a geometric sequence, we can use the formula:
\(an = a1 * r^(n-1),\)
where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.
In this case, we are given a2 = -7 and r = 1/2.
Using the formula, we can find a1 by substituting n = 2:
a2 = a1 * (1/2)^(2-1).
We know that a2 = -7, so we can rewrite the equation:
-7 = a1 * (1/2)^1,
-7 = a1 * (1/2).
Now, let's solve for a1:
a1 = -7 * (2/1),
a1 = -14.
We have found that the first term, a1, is equal to -14.
Now, we can find the seventh term, a7, by substituting n = 7 into the formula:
a7 = (-14) * (1/2)^(7-1),
a7 = (-14) * (1/2)^6,
a7 = (-14) * (1/64),
a7 = -14/64,
a7 = -7/32.
Therefore, the seventh term of the geometric sequence is -7/32.
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Find magnitude of theta. Was told two major things are triangle angles equal 180 and alternate interior angles.
The measure of the angle θ is 30 degrees, or the magnitude of theta is 30 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have a diagram shown in the picture.
The measure of an angle is 30 degrees shown.
The triangle is a right-angled triangle
30-60-90
Two parallel lines are shown which are intersected by a transversal.
The adjacent angle is 60 degrees.
The measure of angle θ:
θ = 90 - 60
θ = 30 degrees
Thus, the measure of the angle θ is 30 degrees, or the magnitude of theta is 30 degrees.
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Using compatible numbers, which of the following is the best estimate for 564 divided by 73? A.8 B.9 C.7 D.6
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sign, 7, point, 50 delivery fee and \$14$14dollar sign, 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under \$60$60dollar sign, 60. Each pizza is cut into 888 slices, and she wonders how many total slices she can afford. Let PPP represent the number of pizzas that Jacque buys.
Answer:
30slicesStep-by-step explanation:
given data
cost of pizza $7.5
cost of delivery=$14
let the the number of pizza be p
let the total cost of x pizza be y
the expression for the total cost of x pizza is
y=7.5+14p
given that y=$60
60=7.5+14p
solving for x we have
14p=60-7.5
14p=52.5
p=52.5/14
p=3.75
therefore the total slices is
3.75*8= 30slices
find the derivative of the function. f(t) = 3^7t/ t
The derivative of the function f(t) = 3^(7t)/ t is 3^(7t)(7ln(3)t - 1) / t^2.
Given function is f(t) = 3^(7t)/ t
To find the derivative of the function, we have to use the formula of quotient rule.
The formula is given as,If y = u/v, then dy/dx = (v du/dx - u dv/dx) / v²
f'(t) = [(t)(d/dt)(3^(7t)) - (3^(7t))(d/dt)(t)] / t^2
The first term requires the chain rule:
(d/dt)(3^(7t)) = (3^(7t))(d/dt)(7t) = (3^(7t))(7ln(3))
Substituting into the formula, we get:
f'(t) = [(t)(3^(7t))(7ln(3)) - (3^(7t))] / t^2
= [3^(7t)(7ln(3))(t) - 3^(7t)] / t^2
Simplifying, we get:
f'(t) = 3^(7t)(7ln(3)t - 1) / t^2
Therefore, the derivative of the function f(t) = 3^(7t)/t is:
f'(t) = 3^(7t)(7ln(3)t - 1) / t^2
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How do you solve this literal equation:
-3x+2c=-3, solve for x
Answer:
x = 1 + 2 c 3
Step-by-step explanation:
PLEASE HELP ME I HAVE NO CLUE HOW TO DO THIS
Answer:
a.
Step-by-step explanation:
5y=p(95°) vertical opposite angles
5x=85° || || ||
5y + 5x + 85° + 95° =360° revolution
What can each term of the equation be multiplied by to eliminate the fractions before solving?
1/2x-5/4+2x=5/6+x
Answer:
The equation
\dfrac{1}{2}x-\dfrac{5}{4}+2x=\dfrac{5}{6}+x
2
1
x−
4
5
+2x=
6
5
+x
consists of five terms, three of them contain fractions. The denominators of these fractions are 2, 4 and 6.
Find the LCM(2,4,6). Since
2=2;
4=2·2;
6=2·3,
then LCM(2,4,6)=2·2·3=12.
Thus, you have to multiply each term of the equation by 12 to eliminate the fractions.
Answer: 12
Graph the line that represents this equation:
3x - 4y = 8
Drawing Tools
Select
Point
Line
X
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10-
4
8
2
S
A
2
2
Delete
++
Answer:
Step-by-step explanation:
On a baseball diamond, the distance from first base to third base is approximately 127 feet. How many inches is the distance from first base to third base
From first to third base, it is 3 3/8 inches in length. 3 3/8 inches, or 127 feet, separate first base from third base.
First- and third-base lines' intersection is the starting point for all measurements taken from home base. An real square with 90-foot sides is what a baseball "diamond" looks like.
How far must the catcher throw from home plate if a runner attempts to steal second base in order to declare the runner "out"? Explain why more runners attempt to steal second base than third base given this information. but 127 feet to second and third base is established. 3 3/8 inches, or 127 feet, separate first base from third base.
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(Thank you) question down there
Val dove 2.5 times farther than her friend.
To represent the difference in depth between Val and her friend, we can subtract their respective depths. Val's depth is -119 feet, and her friend's depth is -34 feet.
The equation to represent the difference in depth is:
Val's depth - Friend's depth = Difference in depth.
(-119) - (-34) = Difference in depth.
To subtract a negative number, we can rewrite it as adding the positive counterpart:
(-119) + 34 = Difference in depth.
Now we can simplify the equation:
-85 = Difference in depth.
The result, -85, represents the difference in depth between Val and her friend. However, since the question asks for how many times farther Val dove compared to her friend, we need to express the result as a multiplication equation.
Let's represent the number of times farther Val dove compared to her friend as 'x'. We can set up the equation:
Difference in depth = x * Friend's depth.
-85 = x * (-34).
To solve for x, we divide both sides of the equation by -34:
-85 / -34 = x.
Simplifying the division:
2.5 ≈ x.
Therefore, Val dove approximately 2.5 times farther than her friend.
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[31pts and brainliest] What is the measurement of angle Z and why?
Answer:
the measure of angle Z is 104
Step-by-step explanation:
the angle z and 76 form a suplementary angle, which they add up to 180.
To find angle z, just subtract 76 from 180.
4
Write the equation of the line in slope-intercept form given the following:
Slope 3, yintercept (0,8)
5
Write the equation of the line in point-slope form given the following:
Point : (-5,2), Slope : -3
1
Show Your Work
Answer:
\bold{\text{Slope (m)}=\dfrac{1}{4}}Slope (m)=41
Step-by-step explanation:
A linear equation is of the form: y = mx + b where
m is the slope
b is the y-intercept (where it crosses the y-axis)
x + 4y = 16
4y = -x + 16
y = -\dfrac{1}{4}x+\dfrac{16}{4}y=−41x+416
y=-\dfrac{1}{4}x+4y=−41x+4
The y-intercept (b) = 4
Next, find the slope given point (4, 5) and b = 4
\begin{gathered}y=mx+b\\\\5=m(4)+4\\\\1=4m\\\\\dfrac{1}{4}=m\\\\\\\\\large\boxed{Slope (m)=\dfrac{1}{4}}\end{gathered}y=mx+b5=m(4)+41=4m41=mSlope(m)=41
before the electronic calculator became widely available, logarithms were used to carry out complicated calculations. true false
True, Logarithms were used extensively for complicated calculations before the electronic calculator became widely available. A logarithm is a mathematical function that helps simplify complex arithmetic operations by converting multiplication and division into addition and subtraction, respectively.
By using logarithms, complex calculations could be broken down into simpler steps and performed more easily. Logarithms were particularly useful in fields such as astronomy, physics, and engineering, where large numbers and complicated formulas were common. However, with the advent of electronic calculators, the use of logarithms for everyday calculations declined. Today, logarithms are still used in certain fields and for specific applications, but they are no longer the primary tool for carrying out complicated calculations.
Before the electronic calculator became widely available, logarithms were used to carry out complicated calculations. Logarithms simplified complex calculations by turning multiplication and division operations into addition and subtraction.
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Jason has applied to be a camp counselor for the summer. The job pays $9 per hour. The equation to re
job is y = 9x, where x is the number of hours he works and y is the total amount he earns,
Mia has applied to be a lifeguard for the summer. The lifeguard job is three days a week with hours and
the table below.
Hours worked
Amount paid
Tuesday
6
$52.50
Thursday
8
$70,00
Saturday
5
$43.75
Which statement best describes the hourly rates?
O The two jobs pay the same hourly rate.
The comparison cannot be made with the information given.
O Jason's camp counselor job pays a higher hourly rate than Mia's lifeguard job.
Jason's camp counselor job pays a lower hourly rate than Mia's lifeguard job.
Answer:
The correct statement is (3).
Step-by-step explanation:
Jason's hourly pay rate as a camp counselor for the summer is:
J = $9 / hour.
The table representing Mia's pay as a lifeguard for the summer is as follows:
Days Hours worked Amount paid
Tuesday 6 $52.50
Thursday 8 $70,00
Saturday 5 $43.75
Compute Mia's hourly rate for Tuesday: \(\frac{\$52.50}{6}=\$8.75\)
Compute Mia's hourly rate for Thursday : \(\frac{\$70.00}{8}=\$8.75\)
Compute Mia's hourly rate for Saturday: \(\frac{\$43.75}{5}=\$8.75\)
Thus, Mia's hourly rate as a lifeguard for the summer is,
M = $8.75 / hour
This implies that Jason's camp counselor job pays a higher hourly rate than Mia's lifeguard job.
Thus, the correct statement is (3).
Answer:
The answer is C because if u multiply 6 by 9 its 54 that's how much Jason gets for 6 hours while on the other hand Mia for six hours gets 52 dollars.
Step-by-step explanation:
can u guys make this a brainlyest answer
sue plans to mix peppermints worth $1.20 per ib with chocolates worth $2.40 per ib to get a 40 ib mix that is worth $1.65 per ib. How much of each should she use
The amount of each ingredient that is peppermints and chocolates will be 25 lb and 15 lb.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Let x be the number of pounds of peppermints and y be the number of pounds of chocolates.
Sue plans to mix peppermints worth $1.20 per lb with chocolates worth $2.40 per lb to get a 40 ib mix that is worth $1.65 per lb. Then the equations will be
x + y = 40 ...1
1.2x + 2.4y = 40 × 1.65
1.2x + 2.4y = 66 ...2
From equations 1 and 2, we have
1.2x + 2.4(40 - x) = 66
1.2x + 96 - 2.4x = 66
1.2x = 30
x = 25
Then the value of y will be
25 + y = 40
y = 15
The amount of each ingredient that is peppermints and chocolates will be 25 lb and 15 lb.
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find the cross product v = a ×b, where a = 〈1, 2, 3〉 and b = 〈3, 5, 8〉
The cross product of vectors a and b is v = 〈1, 1, -1〉.
The cross product of two vectors is a vector that is orthogonal (perpendicular) to both of the original vectors. It is calculated using the determinant of a 3x3 matrix.
Let's consider two vectors a = 〈a1, a2, a3〉 and b = 〈b1, b2, b3. To find the cross product of two vectors, we can use the formula:
v = (a2b3 - a3b2)i + (a3b1 - a1b3)j + (a1b2 - a2b1)k
Given vectors a = 〈1, 2, 3〉 and b = 〈3, 5, 8〉, we can substitute their components into the formula:
v = ((2 * 8) - (3 * 5))i + ((3 * 3) - (1 * 8))j + ((1 * 5) - (2 * 3))k
= (16 - 15)i + (9 - 8)j + (5 - 6)k
= 1i + 1j - 1k
= 〈1, 1, -1〉
Therefore, the cross product of vectors a and b is v = 〈1, 1, -1〉.
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