Step-by-step explanation:
We can use the equation h(t) = -4.9t^2 + vt + h0, where h0 is the initial height of the rock, v is the initial velocity and t is time in seconds, to solve the problem.
h0 = 43 meters (the top of the cliff)
v = 11 meters per second (upwards direction)
To find the time when the rock is 10 meters from ground level, we set h(t) = 10 meters and solve for t:
10 = -4.9t^2 + 11t + 43
0 = -4.9t^2 + 11t + 33
Solving this quadratic equation, we get t = 4.04 seconds or t = 1.37 seconds.
Since the rock is thrown upwards, it will be 10 meters from ground level twice - once on the way up and once on the way down. We can discard the negative time answer as that would correspond to when the rock is thrown from the ground.
Therefore, the rock will be 10 meters from ground level after 4.04 seconds (on the way down).
A student is applying to the University of Florida (UF) and Florida State (FSU).
There is a 40% chance of being accepted at FSU. If the student is accepted at FSU, the probability of being accepted at UF is 60%. If the student is not accepted at FSU there is an 90% chance of non-acceptance at UF.
What is the probability that a student is accepted at FSU or is accepted at UF?
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
To find the probability that a student is accepted at FSU or accepted at UF, we can use the concept of conditional probability and the law of total probability.
Let's denote the events as follows:
A: Accepted at FSU
B: Accepted at UF
We need to find P(A or B), which can be calculated as the sum of the probabilities of each event minus the probability of their intersection:
P(A or B) = P(A) + P(B) - P(A and B)
Given the information provided, we can calculate the probabilities:
P(A) = 0.4 (40% chance of being accepted at FSU)
P(B|A) = 0.6 (60% chance of being accepted at UF if accepted at FSU)
P(B|A') = 0.9 (90% chance of non-acceptance at UF if not accepted at FSU)
P(A and B) = P(A) * P(B|A) = 0.4 * 0.6 = 0.24 (probability of being accepted at both FSU and UF)
Now we can substitute these values into the formula:
P(A or B) = P(A) + P(B) - P(A and B)
= 0.4 + (1 - 0.4) * P(B|A') - P(A and B)
= 0.4 + 0.6 * 0.9 - 0.24
= 0.4 + 0.54 - 0.24
= 0.7
Therefore, the probability that a student is accepted at FSU or accepted at UF is 0.7, or 70%.
PLEASE HELPPPPPPP NEED NOW
Answer:
BC = 24 units
Step-by-step explanation:
This is an isosceles triangle which always has:
two legs that are congruent to each other (i.e., equal),and two angles that are congruent to each other.In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.
Thus, we can find x by setting CA and BA equal to each other:
(3x - 15 = x + 33) + 15
(3x = x + 48) - x
(2x = 48) / x
x = 24
Thus, x = 24
Since the length of BC is x and x = 24, BC is 24 units long.
At what point(s) A through E is the rate of change of f(x) equal to zero?
The points where the rate of change of f(x) equal to zero are A, C and E
How to determine the point where the rates is 0From the question, we have the following parameters that can be used in our computation:
The graph
The point where the rates is 0 are the points where movement is at a constant
using the above as a guide, we have the following:
The points are A, C and E
Hence, the point where the rates is 0 are A, C and E
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When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 9 m/s². When the same force acts upon another object, its acceleration is 6 m/s². What is the mass of this
object?
Step-by-step explanation:
a = k/m or ma = k
using 4 and 9 4* 9 = k = 36
then the equation becomes:
ma = 36
using a = 6
6 * m = 36 shows m = 6 kg
√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E
Answer:
Step-by-step explanation:
To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.
The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.
Using the Pythagorean theorem, we can find the length of the remaining side TH:
TH^2 = TE^2 - HE^2
TH^2 = 4^2 - 4^2
TH^2 = 16 - 16
TH^2 = 0
TH = 0
Therefore, the length of side TH is 0.
HELP I WILL MARK BRAINLIEST AND GIVE 30 POINTS
An English teacher counted the number of misspelled words in a 1000-word essay he assigned to his students. From a group of 49 students, the mean number of misspelled words was 9.1. The distribution of the student population is normal with a variance of 12.25. What is a confidence interval for the mean number of misspelled words in the student population, considering a confidence level of 99.7%? (Use 3 for the Z value in the formula below)
Answer:
C. [7.6, 10.6]
Step-by-step explanation:
To calculate the confidence interval for the mean number of misspelled words in the student population, we can use the confidence interval formula:
[tex]\boxed{CI=\overline{x}\pm z\left(\dfrac{s}{\sqrt{n}}\right)}[/tex]
where:
[tex]\overline{x}[/tex] is the sample mean.z is the confidence level value.s is the sample standard deviation.n is the sample size.Given values:
[tex]\text{Mean}\;\overline{x} = 9.1[/tex][tex]\text{Variance}\;s^2=12.25[/tex][tex]\text{Sample size}\;n=49[/tex]The standard deviation is the square root of the variance:
[tex]s=\sqrt{s^2}=\sqrt{12.25}=3.5[/tex]
The empirical rule states that approximately 99.7% of the data points will fall within three standard deviations of the mean.
Therefore, z-value for a 99.7% confidence level is z = 3.
Substituting these values into the formula, we get:
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{\sqrt{49}}\right)[/tex]
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{7}\right)[/tex]
[tex]CI=9.1\pm 3\left(0.5\right)[/tex]
[tex]CI=9.1\pm 1.5[/tex]
Therefore, the 99.7% confidence limits are:
[tex]CI=9.1-1.5=7.6[/tex]
[tex]CI=9.1+1.5=10.6[/tex]
Therefore, the confidence interval for the mean number of misspelled words in the student population is [7.6, 10.6].
Can someone help me, please???
A hawker bought boxes of tomatoes at R18 per box at the market. He sold all but 5 boxes which went bad, at R25 per box. If he made a profit of R155, how many boxes of tomatoes did he buy?
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
Let's denote the total number of boxes the hawker bought as "x".
The cost of each box is R18, so the total cost of buying "x" boxes is 18x.
He sold all but 5 boxes, so he sold (x - 5) boxes at R25 per box. The revenue from selling these boxes is 25 * (x - 5).
The profit is calculated by subtracting the cost from the revenue, so we have:
Profit = Revenue - Cost
155 = 25 * (x - 5) - 18x
Simplifying the equation:
155 = 25x - 125 - 18x
155 + 125 = 25x - 18x
280 = 7x
Dividing both sides by 7:
x = 280 / 7
x = 40
Therefore, the hawker bought 40 boxes of tomatoes.
What can you say about the y-values of the two functions f (x) = 3 - 3
and g(x) = 7x² - 3?
☐A. The minimum y-value of f(x) is
B. The minimum y-value of g(x) is -3.
C. g(x) has the smallest possible y-value.
D. f(x) has the smallest possible y-value.
SUBMIT
Answer: B. The minimum y-value of g(x) is -3.
Step-by-step explanation:
Based on the given functions:
f(x) = 3 - 3
g(x) = 7x² - 3
The y-value of f(x) is constant at -3, regardless of the value of x. Therefore, f(x) does not have a minimum y-value, and option A is incorrect.
The y-value of g(x) is determined by the quadratic term 7x². Since the coefficient of x² is positive (7), the parabola opens upwards, indicating that g(x) has a minimum y-value. To find the minimum value of g(x), we can look at the vertex of the parabola, which occurs when x = -b/2a in the quadratic equation ax² + bx + c. In this case, a = 7 and b = 0, so the vertex is at x = -0/2(7) = 0. Substituting x = 0 into g(x), we find: g(0) = 7(0)² - 3 = -3 Therefore, the minimum y-value of g(x) is -3, and option B is correct.
Option C, stating that g(x) has the smallest possible y-value, is incorrect because the y-value of g(x) can be larger than -3 depending on the value of x.
Option D, stating that f(x) has the smallest possible y-value, is incorrect because f(x) does not have a minimum y-value as it is constant at -3.
Therefore, the correct answer is B. The minimum y-value of g(x) is -3.
The volume of this triangular prism is 1,170 cubic feet. What is the value of m?
The calculated value of m in the triangular prism is 13
How to calculate the value of m?From the question, we have the following parameters that can be used in our computation:
The triangular prism
Where, we have
Volume = 1170
The volume of the triangular prism is calculated as
Volume = Base area * Height
So, we have
1/2 * m * 18 * 10 = 1170
Evaluate the products
This gives
90m = 1170
So, we have
m = 13
Hence, the value of m is 13
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Copy the axes below.
a) By completing the tables of values to help
you, plot the lines y = 2x + 1 and
y = 10 x on your axes.
b) Use your diagram to find the solution to the
simultaneous equations y = 2x + 1 and
y=2x+1
x012
Y
y = 10-x
x012
Y
= 10 - x.
y =
Y
10
-3 -2 -1
098
7
6
659
-5
-4
3
2
-1-
-2
w
1 2 3 4 5 6 7 8 9 10 x
By completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.
(a) To plot the lines y = 2x + 1 and y = 10 - x, we need to complete the tables of values and then plot the points on the axes.
For the line y = 2x + 1, we can choose some values of x and calculate the corresponding y values:
x | y
0 | 1
1 | 3
2 | 5
For the line y = 10 - x, we can also choose some values of x and calculate the corresponding y values:
x | y
0 | 10
1 | 9
2 | 8
Plot the points (0, 1), (1, 3), and (2, 5) for the line y = 2x + 1, and the points (0, 10), (1, 9), and (2, 8) for the line y = 10 - x on the provided axes.
(b) To find the solution to the simultaneous equations y = 2x + 1 and y = 10 - x,
we need to identify the point(s) where the two lines intersect on the graph.
From the plotted lines, we can see that they intersect at the point (3, 7). Therefore, the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7.
In conclusion, by completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.
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What is the least common denominator of the equation Three-fourths (x minus 3) minus one-half = two-thirds? 2 9 12 36
Answer:
12
Step-by-step explanation:
[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]
We are looking at the denominators of 4, 2 and 3. We are looking for the least common multiple. If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.
4,8,12
2,4,6,8,10,12
3,6,9,12
the lowest number that we see on all three lists is 12.
Help I’m lost somebody please help me
Answer:
l
Step-by-step explanation:
Need help asap please .
Answer: 2011 and 2012
Step-by-step explanation:
GEOMETRY 50POINTS
Find cos Z.
Answer:
cos Z = [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
cos Z = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{10}{26}[/tex] = [tex]\frac{5}{13}[/tex]
Tom's base salary is K720 for 80 hours. Overtime is paid for at time-and-a-half. If he is paid K828 in a certain pay period, how many overtime hours did he work
Answer:
Tom worked approximately 8 overtime hours in the given pay period.
Step-by-step explanation:
triangle PQR was rotated and then dilated by a scale factor of 9 to create P”Q”R”. Which statement explains why triangle PQR is similar to triangle P”Q”R”?
Triangle PQR is similar to triangle P”Q”R” because the rotation and dilation transformations preserve the shape and angles of the original triangle.
The rotation simply changes the orientation of the triangle, but the angles and side lengths remain the same. The dilation scales all the side lengths by a factor of 9, which preserves the ratios of the side lengths and the angles of the original triangle.
Since similarity of two triangles is defined as the correspondence between the angles of one triangle to the angles of another triangle, and the ratio of the lengths of the corresponding sides is constant, PQR is similar to P”Q”R” because the angles of PQR and P”Q”R” are congruent, and the ratio of the lengths of the corresponding sides is the same. This means that PQR and P”Q”R” have the same shape and are therefore similar.
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PLEASE HELP ITS HARD
Answer:
- 8a²
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m - n)}[/tex]
given
[tex]\frac{80a^9}{-10a^7}[/tex]
= [tex]\frac{80}{-10}[/tex] × [tex]a^{(9-7)}[/tex]
= - 8 × a²
= - 8a²
A solid oblique pyramid has a triangular base with a length of 8 inches and a height of 6 inches. The slant height of each triangular face is 10 inches. What is the volume of this pyramid?
a) 160 cubic inches
b) 200 cubic inches
c) 240 cubic inches
d) 280 cubic inches
The correct value of volume of the pyramid is 48 cubic inches.
To find the volume of the solid oblique pyramid, we can use the formula V = (1/3) * Base Area * Height. The base of the pyramid is a triangle, and the height is given as 6 inches.The formula for the area of a triangle is (1/2) * base * height. In this case, the base length is 8 inches and the height is 6 inches. Base Area = (1/2) * 8 * 6 = 24 square inches
Now, we can calculate the volume of the pyramid:
V = (1/3) * Base Area * Height
V = (1/3) * 24 * 6
V = 48 cubic inches
Therefore, the volume of the pyramid is 48 cubic inches.
None of the provided options (a, b, c, d) match the calculated volume of 48 cubic inches. Please double-check the given options or provide the correct options for further comparison.
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What is the average rate of change in f(x) on the interval [5,9]?
A)-1.5
B)6/4
C)4
D)-6
Answer:
A) -1.5
Step-by-step explanation:
We can find the average rate of change of a function over an interval using the formula:
(f(x2) - f(x1)) / (x2 - x1), where
(x2, f(x2)) is the rightmost part of the interval. In this problem, 9 is our x2 and f(x2) is 3 since 3 is the y-coordinate when you plug in 9 for f(x))(x1, f(x1)) is the leftmost part of the interval of the interval.In this case, 5 is our x1 and f(x1) is 9 since 9 is the y-coordinate when you plug in 5 for f(x).Thus, we can plug in (9, 3) for (x2, f(x2)) and (5, 9) for (x1, f(x1)) to find the average rate of change in f(x) on the interval [5,9].
(3 - 9) / (9 - 5)
(-6) / (4)
-3/2
is -3/2.
If we convert -3/2 into a normal number, we get -1.5
Thus, the average rate of change in f(x) on the interval [5,9] is -1.5
Answer:
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
In this case, we need to find the average rate of change on the interval [5, 9], so a = 5 and b = 9.
From inspection of the given graph:
f(5) = 9f(9) = 3Substitute the values into the formula:
[tex]\textsf{Average rate of change}=\dfrac{f(9)-f(5)}{9-5}=\dfrac{3-9}{9-5}=\dfrac{-6}{4}=-1.5[/tex]
Therefore, the average rate of change of f(x) over the interval [5, 9] is -1.5.
GEOMETRY 100 POINTS
solve the following question.
tysm
Answer:
x = 1307
Step-by-step explanation:
We have tan(α) = opposite/adjacent
⇒ tan(48.4) = 1472/x
⇒ x = 1472/tan(48.4)
⇒ x = 1306.9
⇒ x = 1307
cosine rule problem.
Answer:
111
Step-by-step explanation:
a² = b² + c² - 2bc cos A
a² = (7√3)² + (√6)² - 2(7√3)(√6) cos 45°
a² = 49 × 3 + 6 - 14√18 × (√2)/2
a² = 153 - 42
a² = 111
a = √111
a = √n = √111
n = 111
What is the value of x in equation 2/3(1/2x+12)=1/2(1/3x+14)-3
Answer:
x=-24
Step-by-step explanation:
2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)
Evaluate leaving your answer in a standard form 0.0048*0.81 /0.027*0.04
Step-by-step explanation:
When we simplify the expression, we get:
0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)
Using a calculator to evaluate the two fractions separately, we get:
0.0048 / 0.027 ≈ 0.1778
0.81 / 0.04 = 20.25
Substituting these values back into the original expression, we get:
(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25
Multiplying these two values together, we get:
0.1778 * 20.25 ≈ 3.59715
To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:
3.59715 ≈ 3.59715 × 10^(-3)
Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).
Find all values of x are not in the domain of h
Answer:
x = -1, 1
Step-by-step explanation:
The function h(x) is given below:
[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]
The denominator must not equal to 0. Therefore,
[tex]\displaystyle{x^2-1\neq 0}[/tex]
Solve the inequality; factor the expression:
[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]
Hence,
[tex]\displaystyle{x \neq 1,-1}[/tex]
Therefore, x = -1, 1 both are not in the domain of h.
2. (08.05A LC) A scatter plot is shown below: 15 13 12 11 10 9 8 7 6 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Which two ordered pairs can be joined to best draw the line of best fit for this scatter plot? (5 points) O (4, 15) and (10,7) O (1,6) and (6, 0) O (0, 13) and (10, 11) O (0, 13) and (10,0)
Assets Liabilities and Net Worth Reserves $51 Checkable Deposits $140 Loans 109 Stock Shares 130 Securities 100 Property 10 Refer to the accompanying consolidated balance sheet for the commercial banking system. Assume the required reserve ratio is 30 percent. All figures are in billions. If the commercial banking system actually loans the maximum amount it is able to lend, excess reserves will be reduced to
If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:
Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.
Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.
This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.
This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
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Sampling based upon equal probability is called
Select one:
a. Cluster Sampling
b. Probability sampling
c. Stratified random sampling
d. Simple random sampling
e. Systematic sampling
Note: Answer E is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Sampling based upon equal probability is called d. Simple random sampling. The correct answer is d. Simple random sampling.
Simple random sampling is a sampling technique where each individual in the population has an equal probability of being selected for the sample. It is based on the principle of equal probability, ensuring that every element has the same chance of being chosen. This method involves randomly selecting samples without any specific grouping or stratification.
Cluster sampling involves dividing the population into clusters or groups and randomly selecting entire clusters for inclusion in the sample. It does not guarantee equal probability for individual units within each cluster.
Probability sampling is a general term that encompasses different sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. It refers to sampling techniques that rely on random selection and allow for the calculation of probabilities associated with sample estimates.
Stratified random sampling involves dividing the population into distinct strata based on certain characteristics and then selecting samples from each stratum in proportion to their representation in the population. It does not guarantee equal probability of selection for all individuals.
Systematic sampling involves selecting every kth individual from a population list after randomly selecting a starting point. It does not guarantee equal probability of selection for all individuals.
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which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
Answer:
The slope of the graphed line is A. -5
Step-by-step explanation:
Since when we move one step in x direction, we move 5 steps downwards in y direction, so, the slope is,
m = y/x
m = -5/1
m = -5