Answer:
6 miles shorter
Step-by-step explanation:
Right now, Jimmy walked 21 miles. If he had gone diagonally, he would've walked only 15 miles. This is 6 miles shorter than before.
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
a) 6
b) 9
c) 12
d) 27
e) 48
Answer:
b) 9
Step-by-step explanation:
Given: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in [tex]36[/tex] hours.
To Find: If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled.
Solution:
Let the time taken by one machine to fill a certain production alone be[tex]=\text{x}[/tex]
Time taken when three machine operate independently and simultaneously
[tex]\frac{1}{\text{x}}+\frac{1}{\text{x}}+\frac{1}{\text{x}}=\frac{1}{36}[/tex]
[tex]\frac{3}{\text{x}}=\frac{1}{36}[/tex]
[tex]\text{x}=108[/tex] [tex]\text{hours}[/tex]
Let time taken when one additional machine is used [tex]=\text{y}[/tex]
Time when when one additional machine is used
[tex]\frac{1}{108}+\frac{1}{108}+\frac{1}{108}+\frac{1}{108}=\frac{1}{\text{y}}[/tex]
[tex]\frac{4}{108}=\frac{1}{\text{y}}[/tex]
[tex]\text{y}=27[/tex] [tex]\text{hours}[/tex]
it takes [tex]27[/tex] [tex]\text{hours}[/tex] when one additional machine is used
Now,
fewer hours taken when one additional machine is used
[tex]=\text{number of hours taken when three machines are used}-[/tex][tex]\text{number of hours taken when one additional machine is used}[/tex]
[tex]36-27[/tex]
[tex]9[/tex] [tex]\text{hours}[/tex]
in [tex]9[/tex] fewer hours of simultaneous operation the production order can be filled if one additional machine is used
Hence option b) is correct.
A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is it's angle of inclination to the nearest degree?
The inclination angle is 10°
Step-by-step explanation:
The given scenario forms a right angled triangle where the length of ramp is hypotenuse and the rise of ramp is the perpendicular
Given
H = 4.2m
P = 0.7m
We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse
Let x be the angle
then
[tex]sin\ x = \frac{P}{H}\\sin\ x = \frac{0.7}{4.2}\\sin\ x = 0.1666\\x = sin^{-1} (1.666)\\x = 9.59 => 10[/tex]
Hence,
The inclination angle is 10°
Keywords: Trigonometric ratios, Right angled triangle
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The angle of inclination of the wheelchair ramp to the nearest degree is 9 degrees.
[tex]\[ \theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \][/tex]
Given the rise of the ramp is 0.7 m and the run (length) is 4.2 m, we can plug these values into the formula:
[tex]\[ \theta = \arctan\left(\frac{0.7}{4.2}\right) \][/tex]
Now, we calculate the value of θ:
[tex]\[ \theta = \arctan\left(\frac{1}{6}\right) \][/tex]
Using a calculator, we find:
[tex]\[ \theta \approx \arctan(0.1667) \] \[ \theta \approx 9.4623 \text{ degrees} \][/tex]
Rounding to the nearest degree, we get:
[tex]\[ \theta \approx 9 \text{ degrees} \][/tex]
Therefore, the angle of inclination of the wheelchair ramp is approximately 9 degrees to the nearest degree.
A teacher uses a strong slingshot to release an object from the top of a school high in the air. The function a(t)=-16t^2+128t+50 gives the approximate altitude, in feet, of the object t seconds after it is released. How long will it be before the object hits the ground? Round to the nearest second.
Ground: y = 0
- 16t² + 128t + 50 = 0
Apply quadratic equation.
t = 0, 8 (rounded to the nearest second)
8 seconds
The time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).
Explanation:The given function a(t) = -16t^2 + 128t + 50 represents the approximate altitude, in feet, of an object released from the top of a building t seconds after it is released. To find the time it will take for the object to hit the ground, we need to find the value of t when the altitude is 0.
Setting a(t) = 0, we get:
-16t^2 + 128t + 50 = 0
Using the quadratic formula, we can solve for t.
t = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values a = -16, b = 128, and c = 50, we get t = 0.54 s or t = 3.79 s. Since the object is already at a height of 0 at t = 0 (the time of release), the time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).
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A museum employee surveys a random sample of 350 visitors to the museum. If those visitors, 266 stopped at the gift shop. Based on these results, about how many people out of 3200 visitors to the museum would be expected to stop at the gift shop?
Answer: 2432 visitors
Step-by-step explanation:
An employee of a museum surveyed a random sample of 350 visitors that came to the museum. Of the visitors that were surveyed, 266 stopped at the gift shop.
Since 266 out of 350 stopped at the gist shop, we find the fraction or decimal of people who stopped at the gift shop. This will give 266/350 = 19/25 or 0.76.
If 3200 visitors come to the museum, the expected number of people to stop at the gift shop are:
= 0.76 × 3200
= 2432
2432 visitors are expected to stop at the gift shop out of 3200 visitors.
1. Remember what we know about vertical angles and solve for x. (SHOW WORK)
2. Use the figure to answer the questions. (a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain. (SHOW WORK)
Answer:
Ans 1. [tex]x= 7[/tex]
Ans 2.a.
[tex]\overline {AC} \cong \overline {JL} \\\textrm{is the additional information required to prove the triangles are congruent by SAS postulate}[/tex]
Ans.2.b.
[tex]\overline {BC} \cong \overline {KL} \\\textrm{is the additional information required to prove the triangles are congruent by the HL theorem}[/tex]
Step-by-step explanation:
Solution:
1.
Vertically opposite angles are equal.
[tex]\therefore (x+16) = (4x-5)\\\therefore (4x-x) = (16+5)\\\therefore (3x) = (21)\\\therefore x = 7[/tex]
2.a.
proof for Δ BAC ≅ ΔKJL by SAS postulate.
InΔ BAC and Δ KJL
BA ≅ KJ Given
∠ BAC ≅ ∠ KJL {measure each angle is 90}
[tex]\overline{AC} \cong \overline{JL}\ \textrm{additional information require to prove the tangles are congruent by SAS postulate}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Side-Angle-Side postulate...PROVED}[/tex]
2.b.
proof for Δ BAC ≅ ΔKJL by HL theorem.
InΔ BAC and Δ KJL
BA ≅ KJ Given
∠ BAC ≅ ∠ KJL {measure each angle is 90}
[tex]\overline{BC} \cong \overline{KL}\ \textrm{additional information require to prove the tangles are congruent by HL theorem}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Hypotenuse Leg Theorem......PROVED}[/tex]
Manufacture has been selling 1450 television sets a week at $540 each. A market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
a) Find the function representing price as a function of the demand p(x)p(x), where xx is the number of the television sets sold per week and p(x)p(x) is the corresponding price.
Answer:
[tex]p(x)= -\frac{1}{10}x + 685[/tex]
Step-by-step explanation:
Since, Function of demand is the linear function of quantity.
Let x represents the quantity and p represents the price of each unit.
∵ Manufacture has been selling 1450 television sets a week at $540 each,
i.e. [tex](x_1, p_1) = (1450, 540)[/tex]
Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
i.e. [tex](x_2, p_2) = (1580, 527)[/tex]
Thus, the linear equation of the price,
[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]
[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]
[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]
[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]
[tex]p = -\frac{1}{10}x + 145 + 540[/tex]
[tex]\implies p = -\frac{1}{10}x + 685[/tex]
Hence, the function representing price as a function of the demand is,
[tex]p(x)= -\frac{1}{10}x + 685[/tex]
A woman has money in two accounts. One account pays 5% annual interest, whereas the other pays 10% annual interest. If she has $800 more invested in 10% than she does at 5% and her total interest for a year is $250, how much does she have in each account?
Answer:
She have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest
Step-by-step explanation:
Let x be the amount she invested at 5% annual interest
She invested $800 more in 10%
So, she invested x+800 at 10% annual interest
Case 1:
Principal = x
Time = 1 year
Rate of interest = 5%
[tex]Si =\frac{P \times R \times T}{100}[/tex]
[tex]SI=\frac{x \times 5 \times 1}{100}[/tex]
[tex]SI=\frac{5}{100}x[/tex]
Case 2:
Principal = x+800
Time = 1 year
Rate of interest = 10%
[tex]Si =\frac{P \times R \times T}{100}[/tex]
[tex]SI=\frac{(x+800) \times 10 \times 1}{100}[/tex]
[tex]SI=\frac{10}{100}(x+800)[/tex]
Interest = Amount - principal = 880+1.1x-x=880+0.1x
Her total interest for a year is $250
So, [tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]
[tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]
[tex]\frac{5}{100}x+\frac{10}{100}x+80=250[/tex]
[tex]\frac{15}{100}x+80=250[/tex]
[tex]\frac{15}{100}x=250-80[/tex]
[tex]x=170 \times \frac{100}{15}[/tex]
[tex]x=1133.33[/tex]
So the amount she invested at 5% annual interest is $1133.33
She invested at 10% annual interest=x+800=1133.33+800=1933.33
Hence she have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest
The amount she has in the account that an annual interest of 5% is $3400.
The amount she has in the account that an annual interest of 10% is $4,200.
What is the system of linear equations that represent the question?x - y = $800 equation 1
0.1x + 0.05y = $250 equation 2
Where:
x = amout invested in the account that earns a 10% interesty = amout invested in the account that earns a 5% interestHow much was invested in the account that earns a 5% interest?
Multiply equation 1 by 0.1
0.1x - 0.1y = 80 equation 3
Subtract equation 3 from equation 2
0.05y = 170
Divide both sides by 0.05
y = $3,400
How much was invested in the account that earns a 5% interest?
Substitute for y in equation 1
x - 3400 = 800
x = 3400 + 800
x = $4,200
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Suppose a jar contains 9 red marbles and 13 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer in decimal form, rounded to the nearest thousandth.
Answer: P = 0.156
Step-by-step explanation:
Initially in the jar, we have 9 red and 13 blue marbles, so we have a total of 22 marbles in the jar.
If we want to take a red ball for the jar, the probability of getting one is equal to the number of red balls divided by the total number of balls, so:
P1 = 9/22 .
Now, suppose you already took one red ball, we want to take the second one; the probability is calculated in the same way, but now we already took a red ball, so we have 8 red balls and 21 balls in total; so:
P2 = 8/21
Now the probability of both events to happen is equal to the product of their probabilities:
P = P1*P2 = (9/22)*(8/21) = 0.1558
Now we want to round it to the nearest thousandth.
The thousandth is the second number after the decimal point, and the number that comes after is an 8, so we need to round it up; then we get:
P = 0.156, or 15.6% in percentage form.
Find all functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).
Answer:
[tex]y=Ae^{-2x}[/tex]
Step-by-step explanation:
Given that the functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).
Let (x,y) be any arbitrary point of contract
The tangent line passes through two points (x,y) and (x+2,0)
Slope of tangent line = f'(x) = change in y/change in x= [tex]\frac{-y}{2}[/tex]
i.e. we have
[tex]\frac{dy}{dx} =\frac{-y}{2}[/tex]
Separate the variables
[tex]\frac{dy}{y} =-2x\\lny =-2x+c[/tex]
Raise to power e
[tex]y=Ae^{-2x}[/tex]
Thus the functions would have the above form for various values of A
You formally challenge the classification of information and the classifying agency provides a partial response. What is your responsibility if the classifying agency does not provide a full response within 120 days.
Answer:
I will forward the challenge to the ISCAP.
Step-by-step explanation:
If the classifying agency does not provide a full response within 120 days, then as per my responsibility, I will forward the challenge to the ISCAP.
ISCAP is the Inter agency security classification appeals panel.
ISCAP is a deciding panel that decides on certain classification or declassification issues to its users, with a forum for further review.
A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing. What is the largest area that can be enclosed?
Answer:
Area = 2500 square feet is the largest area enclosed
Step-by-step explanation:
A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing
Let x be the length of each box and y be the width of the box
Perimeter of the box= 3(length ) + 4(width)
[tex]200=3x+4y[/tex]
solve for y
[tex]200=3x+4y[/tex]
[tex]200-3x=4y[/tex]
divide both sides by 4
[tex]y=50-\frac{3x}{4}[/tex]
Area of the rectangle = length times width
[tex]Area = 3x \cdot y[/tex]
[tex]Area = 3x \cdot (50-\frac{3x}{4})[/tex]
[tex]A=150x-\frac{9x^2}{4}[/tex]
Now take derivative
[tex]A'=150-\frac{9x}{2}[/tex]
Set it =0 and solve for x
[tex]0=150-\frac{9x}{2}[/tex]
[tex]150=\frac{9x}{2}[/tex]
multiply both sides by 2/9
[tex]x=\frac{100}{3}[/tex]
[tex]A''=-\frac{9}{2}[/tex]
For any value of x, second derivative is negative
So maximum at x= 100/3
[tex]A=150x-\frac{9x^2}{4}[/tex] , replace the value of x
[tex]A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})[/tex]
Area = 2500 square feet is the largest area enclosed
Final answer:
To find the largest enclosed area with 200 feet of fencing divided into 3 plots, solve the equation 2l + 4w = 200 and substitute the value of l into the area formula.
Explanation:
To find the largest area that can be enclosed with 200 feet of fencing and divided into 3 equal plots, we can first find the length of each side of the rectangular piece of land. Let's assume the length of the land is 'l' and the width is 'w'.
Since the land is divided into 3 equal plots, each plot will have a length of l/3 and a width of w.
From the information given, we can form the equation 2l + 4w = 200 (each length side is counted twice and each width side is counted once). We can solve this equation for l and substitute it back into the area formula (A = l * w) to find the largest possible area.
You have family traveling from far away to come to your house for Thanksgiving. If they travel 324 miles and arrive to your house in 6 hours, how fast were they traveling?
Answer: 54 mph
Step-by-step explanation:
Speed x Time = Distance
So, Speed = Distance/Time
Speed = 324 miles/6hrs = 54 mph
Test grades on the last statistics exam had a mean = 78 and standard deviation = .14. Suppose the teacher decides to curve by subtraction 31 from all scores then doubling the values. If Y represents the new test scores, what is the mean and standard deviation of Y?
Answer:
The mean and standard deviation of Y are, 94 and 0.28 respectively.
Step-by-step explanation:
Let the random variable , 'Test grades on the last statistics exam' be X.
Then according to the question,
E(X) = 78 ------------(1)
and
[tex]\sigma_{X}[/tex] = 0.14------------(2)
Now, according to the question,
Y = 2(X - 31)
⇒E(Y) = 2(E(X) - 31)
= [tex]2 \times (78 - 31)[/tex]
= 94 ----------------(4)
and
V(Y) = 4V(X)
⇒[tex]\sigma_{Y} = 2 \times \sigma_{X}[/tex]
⇒[tex]\sigma_{Y} = 2 \times 0.14[/tex] = 0.28
So, the mean and standard deviation of Y are, 94 and 0.28 respectively.
About 20 different comic books will be distributed to five kids. (a) How many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)?
Answer:
5^20
Step-by-step explanation:
For each comic book, there are five different choices for which kid will receive that comic book. 20 decisions are made, one for each comic book with five different possibilities for each choice. The number of ways to distribute the comic books to the five kids is 5^20.
Final answer:
The formula for distributing 20 comic books among five kids with no restrictions is C(24, 5) = 42,504 ways.
Explanation:
To distribute the 20 comic books to five kids with no restrictions on how many each kid receives, we can use the concept of distributing identical items among distinct groups.
The number of ways to distribute the comic books in this scenario is represented by the formula: C(n+r-1, r) where n is the number of items (in this case, 20 comic books) and r is the number of groups (5 kids).
Therefore, the number of ways to distribute the comic books to the five kids is: C(20+5-1, 5) = C(24, 5) = 42,504 ways.
The birth rate of a population is b(t) = 2300e0.024t people per year and the death rate is d(t)= 1450e0.019t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)
To calculate the area between the birth rate and death rate curves for a given time interval, find the net growth rate function by subtracting the death rate from the birth rate, and then integrate this function over the time interval. The result reflects the population surge due to the rates of births and deaths.
Explanation:The student's question involves calculating the area between two exponential growth curves, birth rate and death rate, over a given time interval. To find the area between the curves b(t) = 2300e0.024t and d(t) = 1450e0.019t from t = 0 to t = 10, we need to integrate the difference between them with respect to time over the given interval.Step-by-step Solution:
Subtract the death rate from the birth rate to get the net growth rate function: g(t) = b(t) - d(t) = 2300e0.024t - 1450e0.019t.
Integrate the net growth rate function with respect to t from 0 to 10 to find the total area.
Use a calculator or computer software to perform the integration and round the final answer to the nearest integer.
This computation will give the total number of people added to the population over the 10-year period, which reflects the population surge resulting from the different rates of increase in births and deaths.
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Find the yy-intercept of each line defined below and compare their values.
Answer:
y-intercept: when x = 0
For Line A:
y = 0 + 7 = 7
For line B:
when x = 0, the value is -5
7 > -5, so y-intercept of line A is greater than line B's.
The number of people who enter a drugstore in a given hour is a Poisson random variable with parameter λ = 10 . Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour. What assumptions have you made?
To calculate the conditional probability of at most 3 men entering the drugstore given that 10 women entered using Poisson Distribution. The gender doesn't influence the probability, therefore the events are treated as independent. Assumption made is that occurrences are independent and happen at a known average rate.
Explanation:To compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour, we would apply Poisson Distribution. Poisson Distribution is used to find the probability of a number of events in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event.
However, in this case, the number of men entering is independent of the number of women entering. Therefore, the fact that we know 10 women entered does not affect the probability regarding the number of men. The gender of the individuals entering the drugstore is irrelevant, and we can consider them as independent events. The result is the same if we simply asked: What is the probability that at most 3 people entered the drugstore?
To calculate this, we would use the formula for Poisson Distribution, summing up the probabilities of 0, 1, 2 and 3 events happening. The assumption made here is that the occurrences are independent of each other and occur with a known average rate, λ, which is 10 in this question.
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There are 347 students at a college who have taken a course in calculus, 214 who have taken a course in discrete mathematics and 190 who have taken courses in both calculus and discrete mathematics.
A.How many students have taken a course in either calculus or discrete mathematics?
B.How many have taken calculus but not discrete mathematics?
C.How many have taken discrete mathematuics but not calculus?
Final answer:
There are 371 students who have taken a course in either calculus or discrete mathematics, 157 students have taken calculus but not discrete mathematics, and 24 students have taken discrete mathematics but not calculus.
Explanation:
To determine how many students have taken a course in either calculus or discrete mathematics, we use the principle of inclusion and exclusion. The formula for two sets A (calculus students) and B (discrete mathematics students) is: |A∪B| = |A| + |B| - |A∩B|.
A. Using the provided numbers: |A∪B| = 347 (calculus students) + 214 (discrete mathematics students) - 190 (students in both) = 371 students have taken a course in either calculus or discrete mathematics.
B. The number of students who have taken calculus but not discrete mathematics is found by subtracting the number of students who have taken both from the total number of calculus students: 347 - 190 = 157 students.
C. Similarly, the number of students who have taken discrete mathematics but not calculus is found by subtracting the number of students who have taken both from the total number of discrete mathematics students: 214 - 190 = 24 students.
Suppose a correlation is computed in each of two samples. If the value of SSXY is the same in each sample, and the denominator of the test statistic is larger in Sample 1, then in which sample will the value of the correlation coefficient be larger?
Answer:
Sample 2
Step-by-step explanation:
Correlation is a technique that show strongly pairs of variables.
For example height and width .There are several different correlation techniques .Correlation is determined by dividing product of two variables. standard deviation.Standard deviation is a dispersion of data. Co relation between two variable could be positive or negative or both.
Correlation between two sample is computed. if test statistic is larger in sample 1 then sample 2 will have the larger value of correlation coefficient.
20.There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent , what is the probability that David will eat a healthy breakfast or that it will rain A.20% B.80% C.85% D.95% E.105%
Answer:
A. 20%
Step-by-step explanation:
These events are independent, because if David eats a healthy breakfast cannot influence on would be rain or not.
"And" for probabilities of independent events means "x" (times).
80% = 0.8
25% = 0.25
0.8*0.25 = 0.2 = 20%
The temple at the top of the pyramid is approximately 24 meters above ground, and there are 91 steps leading up to the temple. How high above the ground would you be if you were standing on the 80th step. PLEASE ANSWER QUICK!!!
Answer:
21.10 m
Step-by-step explanation:
Given:
Height of the temple above ground is, [tex]H=24\ m[/tex]
Total number of steps is, [tex]N=91[/tex]
Let us assume that each step is of same height, then the height of each step is given as:
[tex]\textrm{Each step height}=\frac{Total\ Height}{Total\ steps}=\frac{H}{N}=\frac{24}{91}\ m[/tex]
Now, height corresponding to 1 step = [tex]\frac{24}{91}\ m[/tex]
∴ Height corresponding to 80 steps = [tex]\frac{24}{91}\times 80=\frac{24\times 80}{91}=21.10\ m[/tex]
So, I would be at a height of 21.10 m above the ground at the [tex]80^{th}[/tex] step.
determine the intervals on which the function is increasing, decreasing and constant
Answer:
increasing: (-∞, 0)decreasing: (0, ∞)Step-by-step explanation:
The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...
increasing from -∞ to 0 (not including 0)
decreasing from 0 to +∞ (not including 0)
_____
At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.
Given: ∆ABC, AB = 12, AC = 17 Area ∆ABC = 65 Find: BC, m∠A, m∠B, m∠C
Answer:
BC = 10.889m∠A = 39.6°m∠B = 95.8°m∠C = 44.6°Step-by-step explanation:
There are at least a couple of ways you could go at this. Here, we'll use an area formula to find m∠A, then use the law of cosines to find BC. Using BC, we can use the law of sines to find another angle.
Area = (1/2)·AB·AC·sin(∠A)
65·2/(12·17) = sin(∠A) ≈ 65/102
∠A = arccos(65/102) ≈ 39.587°
From the law of cosines, ...
BC² = AB² +AC² -2·AB·AC·cos(∠A)
BC² = 12² +17² -2·12·17·cos(39.587°) ≈ 118.5735
BC ≈ √118.5735 ≈ 10.889
Then ∠C can be found from the law of sines:
sin(∠C)/AB = sin(∠A)/BC
∠C = arcsin(AB/BC·sin(∠A)) ≈ 44.609°
The measure of ∠B will be the angle that makes the total be 180°:
39.587° +∠B +44.609° = 180°
∠B = 95.804°
_____
There is actually another solution, in which ∠A is obtuse. We thought the diagram showed an acute triangle, so we didn't investigate the other alternative. The above calculations show the triangle is obtuse in any event.
See the second attachment for the other solution.
Priya and Han are biking in the same direction on the same path. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many m miles Han has gone after t hours.
m=16t can be used to determine the distance in miles Han has gone after t hours.
Step-by-step explanation:
Speed of Han = 16 miles per hour
Let,
m be the distance covered by Han in miles;
t be the number of hours Han has been biking,
According to formula,
Distance = Speed*Time
[tex]m=16*t\\m=16t[/tex]
m=16t can be used to determine the distance in miles Han has gone after t hours.
Keywords: distance, speed
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Answer:
y = mx + b ( y = 16t + 0
Step-by-step explanation:
A simple random sample of 1200 adult Americans is selected, and each person is asked the following question: "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Only 39% of those responding answered "Yes." This survey ____.
a. is reasonable accurate since it used a large simple random sample.
b. needs to be larger since only about 24 people were drawn from each state.
c. probably understates the percent of people who favor a system of national health insurance.
d. is very inaccurate but neither understates nor overstates the percent of people who favor a system of national health insurance. Because simple random sampling was used, it is unbiased.
e. probably overstates the percent of people who favor a system of national health insurance.
Answer:
c. probably understates the percent of people who favor a system of national health insurance.
Find the slope for each line. And can you show me how you did it.
Answer:
1 : -1
2:2
3:-5
4: 1/2
5: -3
6: -3/2
7: 1/2
8: -1/2
9: 1
10: 1/3
Step-by-step explanation:
well all u have to do is do rise over run, rise/run. find 2 points and go up according to how much it goes up and go left or right based on the graph. AND sometimes the slope will be negative like number 1.
A group of 4 friends decided to go to a soccer game and spend $124. They each bought a ticket to the game and a soda. If each soda cost $6, how much was each ticket to the game?
Answer:
$25 each ticket!
Step-by-step explanation:
6*4=24
124-24=100
100/4=25
A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of fluid ounces and the sample standard deviation is fluid ounces. Find a 95% two-sided confidence interval on the mean volume of syrup dispensed. Assume the population is approximately normally distributed.
Answer:
You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.
Step-by-step explanation:
Calculation
M = 0.96
Z = 1.96
sM = √(0.96)^2/25) = 0.19
μ = M ± Z(sM)
μ = 0.96 ± 1.96*0.19
μ = 0.96 ± 0.3763
Result
M = 0.96, 95% CI [0.5837, 1.3363].
You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.
Bill and susan buy 16 oranges at a fruit stand. They make orange juice using 3/4 of the oranges. How many oranges do bill and susan use to make orange juice?
they use 12 oranges
4•4=16-4=12 which is 3 of the 4/4
The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers but the division is not wholly complete.
As per the given,
They make orange juice using 3/4 of the oranges.
3/4 of 16
(3/4)16 = 3 x 4 = 12 oranges
Hence "The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges".
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The nutrition information on the box of cereal says that a one third cup serving provides 80 calories and six grams of dietary fiber. At that rate find how many calories and grams of fiber are in a half cup serving
Answer:
120 calories and 9 grams of fiber.
Step-by-step explanation:
We are told that 1/3 cup serving contains 80 calories and 6 grams of fiber.
Let's multiply everything by 3. So,
1 cup serving has 3*80 = 240 calories and 3*6 = 18 grams of fiber.
But, we want to really know about 1/2 cup. So, now we multiply everything by 1/2.
1/2 cup has (1/2) (240) = 40 calories and (1/2) (18 grams) = 9 grams of fiber.
Answer:
240 calories and 9 grams of fiber
Step-by-step explanation: