Answer:
Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.
Step-by-step explanation:
Given that,
A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.
From Pythagorean Theorem,
(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+
Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.
∴y²= x²+10²
[tex]\Rightarrow y=\sqrt{x^2+100}[/tex]
Differentiating with respect to t
[tex]\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}[/tex]
[tex]\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}[/tex]
Since the car driving towards the intersection at 13 m/s.
so,[tex]\frac{dx}{dt}=-13[/tex]
[tex]\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)[/tex]
Now
[tex]\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)[/tex]
[tex]=\frac{24\times (-13)}{\sqrt{676}}[/tex]
[tex]=\frac{24\times (-13)}{26}[/tex]
= -12 m/s
Negative sign denotes the distance between the car and the person decrease.
Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.
The rate of change of the distance between the car and the person is [tex]\(-\frac{65}{12}\)[/tex] meters per second, indicating decreasing distance.
To find the rate of change of the distance between the car and the person at the given instant, we can use the concept of related rates. We'll use the Pythagorean theorem to relate the distances involved.
Step 1:
Establish variables.
Let (x) represent the distance the car has traveled north from the intersection, and let (y) represent the distance between the car and the person.
Step 2:
Formulate the equation using the Pythagorean theorem.
[tex]\[x^2 + y^2 = 24^2\][/tex]
Step 3:
Differentiate both sides of the equation with respect to time.
[tex]\[2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0\][/tex]
Step 4:
Plug in the given values and solve for [tex]\(\frac{dy}{dt}\)[/tex].
Given that the car is traveling north, [tex]\(\frac{dx}{dt} = 13\)[/tex]m/s.
When the car is 10 meters east, [tex]\(x = 10\).[/tex]
At that instant, when the car is 24 meters from the intersection, [tex]\(y = 24\).[/tex]
[tex]\[2(10)(13) + 2(24)\frac{dy}{dt} = 0\]\[260 + 48\frac{dy}{dt} = 0\]\[\frac{dy}{dt} = -\frac{260}{48} = -\frac{65}{12}\][/tex]
The rate of change of the distance between the car and the person at that instant is [tex]\(\boxed{-\frac{65}{12}}\)[/tex] meters per second. The negative sign indicates that the distance is decreasing.
find the volume of the cylinder someone help please
Answer:
The answer to your question is in terms of π, Volume = 54π units³
as an exact number Volume = 169.56 units³
Step-by-step explanation:
Data
radius = 3
height = 6
π = 3.14
Process
1.- Look for the formula to calculate the volume of a cylinder
Volume = πr²h
2.- Substitution
Volume = π(3)²(6)
3.- Simplification
Volume = π(9)(6)
4.- Volume in terms of π
Volume = 54π units³
5.- As an exact number
Volume = 54(3.14)
-Result
Volume = 169.56 units³
Use the zero product property to find the solutions to the equation 6x2 – 5x = 56.
O x=-8 or x= 7/6
O х=-8/3 or x = 7/2
O x= -1/2 or x= 56/3
O x = -3/7 or x= 2/3
Please hurry I need the answer ASAP
Answer:
O х= -8/3 or x = 7/2
Step-by-step explanation:
6x² - 5x - 56 = 0
6x² - 21x + 16x - 56 = 0
3x(2x - 7) + 8(2x - 7) = 0
(2x - 7)(3x + 8) = 0
x = 7/2, -8/3
The solutions of the equation 6x² - 5x + 56 using the zero product property is x = -8/3 or x = 7/2.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given is a quadratic expression,
6x² - 5x = 56
We have to find the solutions using zero product property.
Zero product property states that, if a.b = 0, the either a = 0 or b = 0.
Let 6x² - 5x = 56
6x² - 5x - 56 = 0
Dividing throughout by 6,
x² - 5/6 x - 56/6 = 0
We can factorize it as (x + p)(x + q) such that pq = -56/6 and p + q = -5/6.
We know that,
8/3 × -7/2 = -56/6
8/3 - 7/2 = 16/6 - 21/6 = -5/6
So,
x² - 5/6 x - 56/6 = 0
(x + 8/3) (x - 7/2) = 0
Using zero product property,
(x + 8/3) = 0 or (x - 7/2) = 0
x = -8/3 or x = 7/2
Hence the solutions are x = -8/3 or x = 7/2.
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How many times can you expect to roll a 4 if you rolls a fair number cube 120 times? (A fair number cube has 6 sides numbered 1 through 6. If a 4 appears 1 time out of 6 then how many times would it appear out of a 120?)
Answer:
20times
Step-by-step explanation:
A fair of die has 6sides.
If 4 appears 'once' out of a 6.
Then, 4 will appear 2times out of 12 i.e
6faces = 1time
12faces = 2times.
But remember that we want to know how many times 4 will appear out of a 120
120faces = x times
Since 6faces = 1time (i.e 4 occur one time in six faces)
cross multiplying:
6 × x = 120
x = 120/6
x = 20times
This means 4 will appear 20times out of a 120
Schadek Silkscreen Printing Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to be defective.
a. What is the estimated proportion defective in the population?
b. Develop a 95 percent confidenceinterval for the proportion defective.c. Zack has an agreement withhis supplier that he is to return lots that are 10 percent or moredefective. Should he return this lot? Explain your decision.
Given Information:
Number of defective cups = 15
Total number of cups = 300
Required Information:
a) defective proportion = p = ?
b) 95% confidence interval of defective proportion = ?
Answer:
a) defective proportion = p = 0.05 = 5%
b) 95% confidence interval of defective proportion = (2.5%, 7.5%)
Step-by-step explanation:
The estimated defective proportion is given by
p = Number of defective cups/Total number of cups
p = 15/300
p = 0.05
p = 5%
The confidence interval of defective proportion is given by
[tex]CI = p \pm z\sqrt{\frac{p(1-p)}{n} }[/tex]
Where p is the defective proportion, z is the z-score corresponding to 95% confidence level and n is the total number of cups.
The z-score corresponding to 95% confidence level is 1.96
[tex]CI = 0.05 \pm 1.96\sqrt{\frac{0.05(1-0.05)}{300} }[/tex]
[tex]CI = 0.05 \pm 1.96(0.01258)[/tex]
[tex]CI = 0.05 \pm 0.025[/tex]
[tex]Upper = 0.05 + 0.025 = 0.075[/tex]
[tex]Lower = 0.05 - 0.025 = 0.025[/tex]
[tex]CI = (0.025, 0.075)[/tex]
CI = (2.5%, 7.5%)
So that means we are 95% confident that the defective proportion is between 2.5% to 7.5%.
Zack should not return this lot since the defective percentage is below 10%
Final answer:
Zack Schadek calculated the proportion of defective cups to be 5%, and then he developed a 95% confidence interval which did not surpass the 10% defectivity threshold set by his agreement with the supplier. Therefore, he should not return the lot based on this sample's data.
Explanation:
To answer the question of whether Zack Schadek should return the shipment of cups, we first need to calculate the estimated proportion defective in the population. We do this by dividing the number of defective cups by the total number of cups in the sample. In this case, it is 15 defective cups out of 300, which equals 0.05 or 5%.
Next, we will develop a 95 percent confidence interval for the proportion defective. To construct this confidence interval, the binomial distribution can be approximated by a normal distribution since np and n(1-p) are both greater than 5. Plugging in the values, we obtain the confidence interval.
Finally, considering Zack's agreement with his supplier to return lots that are 10% or more defective, the calculated proportion defective is well below 10%. Additionally, since the confidence interval does not include 10% or higher values, Zack should not return the lot based on the data from his sample.
Threa consecutive integers have a sum of 30. Which equation can be used to find x, the value of the smallest of the three numbers?
Answer:
9
Step-by-step explanation:
X+X+1+X+2=30
3x+3=30
-3. -3
3X=27
Divide by 3
X=9
Answer:
x + (x + 1) + (x + 2) = 30
An investment services company experienced dramatic growth in the last two decades. The following models for the company's revenue R and expenses or costs C (both in millions of dollars) are functions of the years past 1990. R(t) = 21.4e0.131t and C(t) = 18.6e0.131t (a) Use the models to predict the company's profit in 2020. (Round your answer to one decimal place.)(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990
Answer: a) 138.32 and b) 35 years approx.
Step-by-step explanation:
Since we have given that
[tex]R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}[/tex]
So, Profit is given by
[tex]Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}[/tex]
Difference in years of 1990 and 2020=30
So, Profit becomes :
[tex]P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32[/tex]
(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.
So, profit doubles , we get :
[tex]138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t[/tex]
Hence, a) 138.32 and b) 35 years approx.
Final answer:
(a) To predict the company's profit in 2020, substitute the given revenue and cost functions into the profit equation. Calculate the value of the profit at t = 30. (b) To find the time it takes for the profit to double, set the profit equation equal to twice the profit in part (a) and solve for t.
Explanation:
(a) To predict the company's profit in 2020, we need to calculate the difference between the revenue and expenses. The profit (P) is given by the equation P(t) = R(t) - C(t), where R(t) is the revenue function and C(t) is the cost function. Substituting the given functions into the equation, we have P(t) = 21.4e0.131t - 18.6e0.131t. To find the profit in 2020 (t = 30), we plug in t = 30 into the equation and calculate the value of P(30).
(b) To find the time it takes for the profit to double, we need to determine when P(t) is equal to twice the profit in part (a). We set P(t) = 2P(30) and solve for t.
What does automation mean in this sentence The automation telephone answering surveyed frustrated many people
Answer:
Automation means something that does not require human input, automatic.
Answer:
answer is the use of machines that function on their own.
Step-by-step explanation:
Use the Divergence Theorem to evaluate the following integral S F · N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = 2(x???? + y???? + z????) S: z = 0, z = 4 − x2 − y2
Answer:
Result;
[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi[/tex]
Step-by-step explanation:
Where:
F(x, y, z) = 2(x·i +y·j +z·k) and
S: z = 0, z = 4 -x² - y²
For the solid region between the paraboloid
z = 4 - x² - y²
div F
For S: z = 0, z = 4 -x² - y²
We have the equation of a parabola
To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)
We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by
[tex]N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }[/tex]
Solving we have;
[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}[/tex]
Plugging the values for N₁ and N₂, we have
[tex]= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}[/tex]
Where:
F(x, y, z) = 2(xi +yj +zk) we have
[tex]= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA[/tex]
[tex]= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA[/tex]
[tex]= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy[/tex]
[tex]= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy[/tex]
= 32π.
What is the range of the function represented by the graph?
Answer:
y ≥ 1
Step-by-step explanation:
Hence, range of given parabola is y[tex]\geq 1[/tex]
What is parabola ?
A parabola is a curve in which all points are at the same distance from two fixed points: the focus and the origin. a constant straight line (the directrix )
How to solve?
Generic equation of parabola y=p. (x−h[tex])^{2}[/tex]+k where (h,k) denotes the vertex. where parabola has range y[tex]\geq 0[/tex]. but as this curve is shifted at 0,1 hence range becomes y[tex]\geq 1[/tex]
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Identify the surface whose equation is given. rho2(sin2(φ) sin2(θ) + cos2(φ)) = 49
Answer:
The surface is a cylindrical surface with radius 7 units
Step-by-step explanation:
The equation is properly written as:
[tex]\rho^{2} (sin^{2} \phi sin^{2} \theta + cos^{2} \phi) = 49[/tex]
The above equation takes the form [tex]y^{2} + z^{2} = r^{2}[/tex]
Where [tex]y^{2} = \rho^{2} sin^{2} \phi sin^{2} \theta[/tex]
[tex]y = \rho sin \phi sin \theta[/tex]
and [tex]z^{2} = \rho^{2}cos^{2} \phi[/tex]
[tex]z = \rho cos \phi[/tex]
[tex]r^{2} = 49[/tex]
r = 7 units
The surface is a cylindrical surface with radius 7 units
Find the angle measure in degrees
Answer:
82°
Step-by-step explanation:
By inscribed angle theorem:
[tex]m\angle QRP = \frac{1}{2} \times 164 \degree \\ \\ \huge \red{ \boxed{\therefore \: m\angle QRP =82 \degree}}[/tex]
which equation represents a circle with a center at (2,-8) and a radius of 11
Answer:
(x - 2)² + (y + 8)² = 121
Step-by-step explanation:
circle: (x – h)² + (y – k)² = r² (h , k) center r: radius
h = 2 k = - 8 r = 11
equation: (x - 2)² + (y + 8)² = 121
The equation of circle can be determine by using general equation of circle.
The equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].
Given:
The center of circle is [tex](2,-8)[/tex].
The radius is [tex]11[/tex].
Write the general equation of circle.
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
Where, [tex](h,k)[/tex] is center of circle and [tex]r[/tex] is the radius of the circle.
Substitute [tex]2[/tex] for [tex]h[/tex], [tex]-8[/tex] for [tex]k[/tex] and [tex]11[/tex] for [tex]r[/tex] in above equation.
[tex](x - 2)^2 + (y + 8)^2 = 121[/tex]
Thus, the equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].
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which is true about rational numbers
Answer:
a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Step-by-step explanation:
Answer:
Any number that can be written in fraction form is a rational number.
Step-by-step explanation:
Chelsea and Pedro manipulated the rational expression \dfrac{14k^3 + 7k^2}{7k^3 + 14k^2} 7k 3 +14k 2 14k 3 +7k 2 start fraction, 14, k, cubed, plus, 7, k, squared, divided by, 7, k, cubed, plus, 14, k, squared, end fraction. Their responses are shown below.
Answer:
Step-by-step explanation:
[tex]\frac{14k^3+7k^2}{7k^3+14k^2} =\frac{7k^2(2k+1)}{7k^2(k+2)} =\frac{2k+1}{k+2}}[/tex]
Answer:
Both Chelsea and Pedro wrote an expression that is equivalent to the original expression
Step-by-step explanation:
first simplify the expression 14k^3 + 7k^2 / 7k^3 + 14k^2 can you get Chelsea's expression. If you simplify Pedro's equation you get the same expression as Chelsea's
Each baseball team in a baseball league has 14 players. A total of 56 players signed up to play. If t represents the number of teams in the league which statement is true?
Answer:
56 player divided by 14 on each team
Step-by-step explanation:
There will be 4 teams
What is a linear function f for f(-4)=2,f(6)=3
Answer:
y - 3 = (1/10)(x - 6)
Step-by-step explanation:
Note how x (the "run") increases by 10 and how y (the "rise") by 1. Thus, the slope of the line connecting point (-4, 2) with point (6, 3) is
m = rise / run = 1/10.
Using the point-slope equation of a straight line, we derive the equation of this particular line as follows:
y - 3 = (1/10)(x - 6)
Use the Law of Sines to complete an expression that represents the angle measure x.
Answer:
sine (x) / 14.9 = sine (71) / 25.5
sine (x) = 14.9 * sine (71) / 25.5
sine (x) = 14.088248 / 25.5
sine (x) = 0.5524803137
Angle (x) = arc sine(0.5524803137)
Angle (x) = 33.537 degrees
Step-by-step explanation:
The expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].
What is the law of sine?The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).
It can be given as,
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.
For the given problem it can also be given as,
[tex]x^o=\sin^{-1}\left(\dfrac{a\sin B}{c}\right)[/tex]
Put the values,
[tex]x^o=\sin^{-1}\left(\dfrac{(14.9)\sin (71)}{25.5}\right)\\x^o=\sin^{-1}\left(0.5523\right)\\x^o=33.54^o[/tex]
Thus, the expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].
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What is the side length of a cube with a volume of 64 mm??
Cube V= 53
Answer:
side length= 4 mm
Step-by-step explanation:
The explanation is pretty easy;
You know that to get the volume of a cube the formula is length times width times height. You also know that all sides of a cube are equal. so what multiplied by itself 3 times = 64?
That would be 4; 4 times 4 = 16 then 16 times 4 = 64
Sorry if the explanation wasn't great:(
On a beach trip lucy rents a bike from wheel by the waves where they rent bikes for $12 plus $3 per hour if lucy spent $30 how many hours(h) did she ride a bike
Answer:
6 hours
Step-by-step explanation:
Make an equation
Each hour costs $3, and there is a $12 cost regardless of the hours. We know that Lucy spent $30.
3h+12=30
Subtract 12 from both side s
3h=18
Divide both sides by 3
h=6
So, she rented it for 6 hours
Flying against the wind, an airplane travels 4560 kilometers in 6 hours. Flying with the wind, the same plane travels 3720 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
The speed rate of the plane in still air is 1006.67 km/h
The speed rate of the wind is 246.67 km/h
Step-by-step explanation:
To answer the question, we let the speed of the plane in still air = x km/h
Let the speed of the wind = y km/h
Therefore,
4560/(x - y) = 6 hours and
3720/(x + y) = 3 hours
4560 = 6·x - 6·y.........(1)
3720 = 3·x + 3·y ........(2)
Multiplying equation (2) by 2 and add to (1) gives
12080 = 12·x
x = 12080/12 = [tex]1006\frac{2}{3}[/tex] km/h
Substituting the value of x in (1) gives
4560 = 6040 - 6·y
6·y = 1480
y = 1480/6 = [tex]246\frac{2}{3}[/tex]
The speed rate of the plane in still air = 1006.67 km/h
The speed rate of the wind = 246.67 km/h.
If two equations in a linear system have the same slope and the same -intercepts, the system will have:'
a ; infinite solutions
b ; no solution
c ; one solution
d ; two solutions
Answer:
The answer to your question is a. Infinite solution
Step-by-step explanation:
When two lines have the same slope and the same intercepts, this means that these lines are the same so they system of equations will have infinite solutions.
If the lines do not cross, there will be no solution.
If the lines cross in one point there will be one solution
If there are a quadratic and a linear function they will cross in two points.
Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 62.5 3 t + 75.8, where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters.
Final answer:
To determine the age of an elephant with a shoulder height of 300 centimeters, the given formula h = 62.5t + 75.8 is used. Subtracting 75.8 from 300 and then dividing by 62.5 yields the elephant's age as approximately 3.59 years.
Explanation:
The student is asking to determine the age of an Asian elephant based on a mathematical model for its shoulder height. Given the model h = 62.5t + 75.8, and knowing the elephant's shoulder height is 300 centimeters, we can set up the equation as follows:
300 = 62.5t + 75.8
To solve for t, we first subtract 75.8 from both sides:
224.2 = 62.5t
Then, we divide both sides by 62.5:
t = 224.2 / 62.5
t = 3.5872
Therefore, the age of the elephant is approximately 3.59 years.
The elephant is about 46.16 years old.
To find the age of the elephant given its shoulder height, we need to solve the equation for t . The equation given is:
[tex]h = 62.5\sqrt[3]{t} + 75.8[/tex]
Given h = 300 centimeters, we substitute h into the equation and solve for t :
[tex]300 = 62.5\sqrt[3]{t} + 75.8[/tex]
First, isolate the cube root term:
[tex]300 - 75.8 = 62.5\sqrt[3]{t} \\\\ 224.2 = 62.5\sqrt[3]{t}[/tex]
Next, divide both sides by 62.5:
[tex]\sqrt[3]{t} = \frac{224.2}{62.5} \\\\ \sqrt[3]{t} \approx 3.5872[/tex]
Now, to solve for t , cube both sides:
[tex]t \approx (3.5872)^3 \\\\ t \approx 46.16[/tex]
So, the elephant is about 46.16 years old.
The complete question is:
Biologists have discovered that the shoulder height (in centimeters) of a male Asian elephant can be modeled by [tex]h = 62.5\sqrt[3]{t} + 75.8[/tex], where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters. Round your answer to the nearest tenth.
The elephant is about ____ years old.
On Friday, a local hamburger shop sold a combined total of 294 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
98 hamburgers were sold on Friday.
Step-by-step explanation:
294/3=98
98+98=196 cheese burgers
196+98=294 hamburgers and cheeseburgers in total
98 hamburgers
8x + 7 = 2x + 37 ????
Answer: 5
Step-by-step explanation:Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
7 + 8x + -2x = 37 + 2x + -2x
Combine like terms: 8x + -2x = 6x
7 + 6x = 37 + 2x + -2x
Combine like terms: 2x + -2x = 0
7 + 6x = 37 + 0
7 + 6x = 37
Add '-7' to each side of the equation.
7 + -7 + 6x = 37 + -7
Combine like terms: 7 + -7 = 0
0 + 6x = 37 + -7
6x = 37 + -7
Combine like terms: 37 + -7 = 30
6x = 30
Divide each side by '6'.
x = 5
Simplifying
x = 5
I have no clue how to do this
Answer:
14
Step-by-step explanation:
5x + 12 = 7x - 16
28 = 2x
14 = x
Angle 3's alternate interior angle is Angle 2. Angle two is equal to angle 4 (thi is just a rule in geometry). So that means Angle 3 is also equal to angle $. So just make the equations equal to eachother and solve for x as shown above.
Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. How many additional students would Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence?
Answer:
1727 students
Step-by-step explanation:
Here we have the formula for sample size given as
[tex]n = \frac{p(1-p)z^2}{ME^2}[/tex]
Where:
p = Mean
ME = Margin of error = 3
z = z score
Therefore, we have
p = 150/240 = 0.625
z at 99 % = 2.575
ME = [tex]\pm[/tex]3%
Therefore [tex]n = \frac{0.625(1-0.625)2.575^2}{0.03^2} = 1726.73[/tex]
The number of students Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence = 1727 students.
Toby invested £4500 for 2 years in a saving accounts . he was paid 4% per annum compound interest .
How much did Toby have in his saving account after 2 years ?
Final answer:
Toby will have £4867.20 in his savings account.
Explanation:
To determine how much Toby will have in his savings account after 2 years with a 4% per annum compound interest rate, we can use the formula for compound interest:
A = P(1 + r)ⁿ
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of years the money is invested.Given:
Toby's initial investment (P) is £4500.The annual interest rate (r) is 4%, or 0.04 when expressed as a decimal.The money is invested for n = 2 years.Using these values in the formula:
A = £4500(1 + 0.04)²
A = £4500(1.04)²
A = £4500(1.0816)
A = £4867.20
Therefore, Toby will have £4867.20 in his savings account after 2 years.
Shelia deposited $800 into an account that earned 3% simple interest. She did not make any other deposits or withdrawals. After 5 years how much interest did Sheila earn?
Answer:
Sheila earned $120 in interest.
Step-by-step explanation:
In order to calculate the interest earned by Sheila we can use the simple interest formula shown bellow:
i = P*r*t
Where i is the interested earned, P is the amount invested, r is the interest rate and t is the total time. For this case we have:
i = 800*0.03*5
i = 24*5
i = 120
Sheila earned $120 in interest.
Answer: After 5 years, Sheila earns $120
Step-by-step explanation: The calculation of simple interest is given as
Interest = P x R x T
Where P = the amount invested initially (800), R = the rate of interest earned (3% or 0.03) and T = the number of years (5) investment was held
The interest she earned can now be calculated by substituting for the known values as follows;
Interest = 800 x 0.03 x 5
Interest = 120
Therefore after 5 years, Sheila earns $120
Cheryl wants to find the number of hours seventh-graders do homework each week. There are 297 girls and boys in
seventh grade. Which is the best way for Cheryl to get a representative sample without spending too much time?
She can survey 15 of her friends in the school.
She can survey every sixth-grade student in the school.
She can randomly survey 50 girls in the entire school.
She can randomly survey 50 seventh-graders in the school.
Answer: She can randomly survey 50 seventh-graders in the school.
Step-by-step explanation: To get the best result without wasting to much time means she cannot afford to survey every student. To receive the best results it should be unbiased so random is the way to go. Randomly surveying 50 girls in her school does not guarantee that those girls are all seventh graders so the best answer is She can randomly survey 50 seventh-graders in the school.
10 customers entered a store over the course of 5 minutes. At what rate were the
customers entering the store in customers per minute?
Answer:
like 2 per minute?
Step-by-step explanation:
The rate at which customers are entering the store is calculated by dividing the number of customers by the time it took them to enter. In this case, 10 customers entered the store over 5 minutes, so the rate is 2 customers per minute.
Explanation:The rate at which customers are entering the store is calculated by dividing the total number of customers by the total time it took for them to enter. Here, the total number of customers is 10, and the total time is 5 minutes. So, the calculation would be: 10 customers / 5 minutes. This equals 2 customers per minute. Therefore, the rate of customers entering the store is 2 customers per minute.
Learn more about Rate of customers here:https://brainly.com/question/33900981
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