To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.
specify the solid volume?How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.
For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:
V = l × w ×h
The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.
Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.
V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.
We arrive at a total volume of 792 cubic meters by adding these volumes together.
To the nearest hundredth=904.600 cubic meters.
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Matthew is working two summer jobs, making $9 per hour babysitting and making $13 per hour landscaping. In a given week, he can work a maximum of 16 total hours and must earn at least $180. If Matthew worked 3 hours babysitting, determine the maximum number of whole hours landscaping that he can work and still meet his requirements. If there are no possible solutions, submit an empty answer.
Answer:
Step-by-step explanation:
3 hours of babysitting = $27
if he needs $180 per week he needs to work at least 12 hours in landscaping.
12 hours of Landscaping = $156
156 + 27 = 183
It cuts down about an hour of work.
If I misunderstood something, please let me know. Have a good day :)
Please help with trigonometry
14.4 is the value of x in triangle .
What is known as a triangle?
Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. 180 degrees is the sum of the triangle's three angles.
Triangular shapes have three vertices, three angles, and three sides. 180 degrees is the sum of a triangle's three interior angles. The length of a triangle's two longest sides added together exceeds the length of its third side.
17² = 9² + X²
289 = 81 + x²
289 - 81 = x²
208 = x²
x = √208
= 14.4
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m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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A 28-year-old females pays $163 for a 1 year $200,000 life insurance policy what is the expected value of the policy for the policyholder?
Assuming that the policyholder is healthy and has an average life expectancy, we can estimate the expected value of the policy by multiplying the probability of dying during the policy period by the amount that will be paid out in the event of death.
The probability of dying during the policy period can be estimated using actuarial tables, which provide information on life expectancies based on age, gender, and other factors. For a healthy 28-year-old female, the probability of dying during a one-year policy period is very low, likely less than 0.1%.
If we assume a probability of dying of 0.1%, the expected value of the policy would be:
Expected value = 0.001 x $200,000 = $200
This means that, on average, the policyholder can expect to receive $200 in benefits from the policy. However, it's important to note that this is just an estimate and actual benefits may be higher or lower depending on the policyholder's individual circumstances.
Alicia took a friend for a birthday dinner. The total bill for dinner was $44.79 (including tax and a tip). If Alicia paid a 21.6% tip, what was her bill before adding the tip?
(Round your answer to the nearest cent.)
Answer: 27.33
Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze
AC has endpoints A (3,6) and C (-2, 10). What is the length of AC ?
A box contains 16 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
a. The probability is.
(Type a fraction. Simplify your answer.)
***
The probability of selecting all defective transistors is 1/560.
To find the probability of the statementsThe probability of selecting all defective transistors can be calculated as:
P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)
The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:
total number of ways = number of combinations of 3 transistors out of 16
= (16 choose 3)
= 560
Therefore, the probability of selecting all defective transistors is:
P(all defective) = 1 / 560
To simplify the answer, we can write it as a fraction in lowest terms:
P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560
Therefore, the probability of selecting all defective transistors is 1/560.
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I can’t seem to figure this question out
The total surface area of the pyramid is:260 ft²
What is the total surface area of the Pyramid?The area of a triangle is expressed as:
A = ¹/₂bh
where:
b denotes the base of the triangle
h denotes the height of the triangle
Area of rectangle is:
A = l * w
where:
l denotes the length of the rectangle
w denotes the width of the rectangle
Thus, the total surface area of the given pyramid is:
Total Surface Area = 4(¹/₂(10 * 12)) + (10 * 10)
Total Surface Area = 240 + 20
Total Surface Area = 260 ft²
Therefore, we can conclude that is the calculation of the total surface area of the composite figure.
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mathematics plssssssss help me!!!!
correct me
Answer:
let the children be x
let the dog be y
for the heads
x+y = 14 --- eqn 1
for the legs
2x + 4y = 40 ----- eqn2
since the children have 2 legs each and the dogs have 4 legs each
x + y = 14
2x+4y=40
through elimination method
multiply eqn1 by 2 and multiply eqn2 by 1
2x + 2y = 28
2x + 4y = 40 , then subtract
-2y = -12
to get y divide both sides by -2
y = 6
since in eqn 1
x+y=14
x = 14-y = 14-6 = 8
x = 8, y = 6
the children are 8 while the dogs are 6
Please help will give a lot of points
Answer:
how many points will you give?
Step-by-step explanation:
use logb28
PLEASE HELP SOLVE!! 30 PTS!!
Answer:
logb28 ≈ 1.634.
Step-by-step explanation:
logb28 = (log428)/(log47)
We can then substitute the given values for logb4 and logb7:
logb28 = (log428)/(log47) = (log28)/(log24 + log27) = (log28)/(1.386 + 1.946)
1.386+1.946=3.332
logb28/3.332
logb28 ≈ 1.634.
Answer:
[tex]log_b28=3.332[/tex]--------------------
Given:
[tex]log_b 4 = 1.386\ and\ bog_b7=1.946[/tex]Use the following identity to find [tex]log_b28[/tex]:
[tex]log_a(bc)=log_ab+log_ac[/tex]Apply the identity to the given:
[tex]log_b28=log_b(4*7)=log_b4+log_b7=1.386+1.946=3.332[/tex]5. Find the area of the kite.
18 m
-21 m-
Answer: 189 m^2
Step-by-step explanation:
Area = (Diagonal 1 x Diagonal 2) ÷ 2
Rationalize the denominator and simplify:
4/4+√x
Answer: 16-4√x/16-x is the answer.
Step-by-step explanation:
=> 4/4+√x*4-√x/4-√x
=> 4(4-√x)/(4)²-(√x)² {using identity - (a+b) (a-b)=a² - b²}
=> 16-4√x/16-x
x + 5 < 7
x + 5 -? ? 7-?
x ??
<----—------————————--->
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
Graph the solution after you get your answer
The inequality can be solved to get x < 2, the graph is on the image at the end.
How to solve and graph the inequality?Here we have the inequality.
x + 5 < 7
To solve this, we need to isolate the variable, subtracting 5 in both sides we will get.
x < 7 - 5
x < 2
The graph of this inequality will be a number line with an open circle at x = 2, and an arrow that extends to the left side (because x is smaller than 2)
Then we will get the graph that you can see in the image at the end.
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The sequence is geometric.
1, 6, 30, 60, . . .
The sequence 1, 6, 30, 60, . . . is not a geometric sequence
Checking if the sequence is geometricFrom the question, we have the following parameters that can be used in our computation:
1, 6, 30, 60, . . .
To check if the sequence is geometric, we calculae the common ratio of the sequence using
r = next term/previous term
Using the above as a guide, we have the following:
r = 6/1 = 6
r = 30/6 = 5
r = 60/30 = 2
The common ratios of the sequence calculated above are different
This means that the sequence is not geometric
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find the value of x in the cube
Answer:
3√3 ft or 5.20 ft
Step-by-step explanation:
The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.
x = L × √3
x = 3 × √3
x = 3 × 1.7
x = 5.20 ft
I need the answers and a explanation if possible
Wwe can reject the null hypothesis and deduce that there is sufficient empirical evidence to validate the presumption that seatbelts are competent for mitigating fatalities.
How to explain the hypothesisNull Hypothesis: There is no discernible distinction between the proportion of fatalities among occupants wearing seat belts and those without.
Alternative Hypothesis: The portion of fatalities experienced by those in vehicles donning seatbelts will be demonstrably lower in comparison to individuals not utilizing them.
The z-value was computed, finding that (0.0113 - 0.0024) / √(0.0047 * (1 - 0.0047) * (1/2915 + 1/7848)) = 12.43.
For a two-tailed test at a 0.05 significance level with 2915 plus 7848 less 2 = 10761 degrees of freedom, the critical value range would be ±1.96. With the calculated z-value of 12.43 surpassing the critical threshold, we can reject the null hypothesis.
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How to write 1/4 (x-12) in words
Answer:
To write 1/4 (x - 12) in words, you would say "one-fourth of the quantity obtained by subtracting 12 from x."
What are the period and amplitude of the function?
Answer:
period : π ; amplitude : 2
Step-by-step explanation:
Correct me if I'm wrong!!
Find the sum of the arithmetic sequence: 7+11+15+19+...+83+87.
The sum of the arithmetic sequence is 987
What is arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.
For example, the sequence, 2,4,6,8,10... is an arithmetic sequence.
The sum of an arithmetic sequence is given as;
Sn=n/2[2a+(n−1)d]. Where d is the common difference and a is the first term.
the last term is 87
therefore;
87= 7+(n-1) 4
87= 7+4n-4
91-7 = 4n
84 = 4n
n = 84/4
n = 21
therefore 87 is the 21st term
Sn=n/2[2a+(n−1)d]
= 21/2(2×7+(21-1)4
= 21/2 ( 14+80)
= 21×94/2
= 987
therefore the sum of the arithmetic sequence is 987
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Please help me , I don't understand the question..
The test statistic z ≈ -2.59 falls into the rejection region (z < -1.96).
Therefore, we reject the null hypothesis (H₀) in favor of the alternative hypothesis (H₁).
How to solvea) Null and alternative hypothesis:
The null hypothesis (H₀) states that there is no significant difference between the claimed weekly production volume and the actual production volume.
The alternative hypothesis (H₁) states that there is a significant difference between the claimed weekly production volume and the actual production volume.
H₀: μ = 370 units (the claimed weekly production volume is true)
H₁: μ ≠ 370 units (the claimed weekly production volume is not true)
b) Critical value:
Since we're using a two-tailed test at α = 0.05 significance level, we'll look for the critical value (z-score) that corresponds to the 2.5% in each tail (5% total) of the standard normal distribution.
The critical value for a two-tailed test at α = 0.05 is ±1.96. The rejection region consists of the areas where the z-score is less than -1.96 or greater than 1.96.
c) Test statistic:
To calculate the test statistic, we will use the following formula:
z = (X - μ) / (σ / √n)
z = (355 - 370) / (19 / √30) = -15 / (19 / √30) ≈ -2.59
d) Conclusion:
The test statistic z ≈ -2.59 falls into the rejection region (z < -1.96).
Therefore, we reject the null hypothesis (H₀) in favor of the alternative hypothesis (H₁).
This means that there is significant evidence to suggest that the claimed weekly production volume of 370 units is not true.
The Vice President's suspicion about the statement appears to be correct, and further investigation should be conducted to determine the actual production volume.
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50 Points! Multiple choice algebra question. Find the domain and range of the function whose graph is shown. Photo attached. Thank you!
Answer:
"B". Domain is all real numbers, and the Range is all positive real numbers
Step-by-step explanation:
It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form [tex]y=a*b^x[/tex] where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.
Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).
The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.
The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.
Since "a" is positive, the Range is positive numbers only.
Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.
Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero". There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0". So, the Range is written as { y | y>0 }.
Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.
Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"
Can anyone help me answer this question?
1. What is the derivative of sin(x)cos(x)?
2. What is the derivative of sin2(x)cos2(x)?
Answer:
cos 2x
f(x)=4•sin(x)•cos(x)
Step-by-step explanation:
a ups dispatcher sends a delivery truck to 10 different locations. if the truck stops at each location only once, how many different routes are possible
Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.
What is factorial notation?Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.
Here,
The number of different routes possible for the delivery truck can be calculated using factorial notation.
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
This simplifies to:
10! = 3,628,800
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2. Kyle submits a design for the contest, but his explanation was misplaced. How can Figure A be mapped onto Figure B? Can any other transformation be used to map Figure A onto Figure B?
help please i have 5 min
Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.
What is dilation?A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.
The original point of figure A which has 4 points are
(0,02)
(-1, 2)
(0, 1)
(1, 2)
Multiply all th e points by 3, and you get,
(0,02) x 3 = (0, -6) =
(-1, 2) x 3 = (-3, 6)
(0, 1) x 3 = (0, 3)
(1, 2) x3 = (3, 6)
Plotting the new values will give us the transformation (dilation) required. See the attached image.
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Given that X is a normal random variable with a mean of 40 and a standard deviation of 8 what is P (34
The probability is given as follows:
P(34 < X < 46) = 0.5468 = 54.68%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 40, \sigma = 8[/tex]
The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:
Z = (46 - 40)/8
Z = 0.75
Z = 0.75 has a p-value of 0.7734.
Z = (34 - 40)/8
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
Hence:
0.7734 - 0.2266 = 0.5468 = 54.68%.
Missing InformationThe probability is:
P(34 < X < 46).
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0.0625 What is the equivalent percent? %
Answer:6.25%
Step-by-step explanation:
Each day for 47 days, Zara predicted whether or not it would snow.
The frequency tree below shows her predictions and whether it snowed or not.
On what fraction of the days when it snowed was Zara's prediction correct?
Give your answer in its simplest form.
Predicted weather
Snow
No snow
19
Actual weather
Snow 15
No snow
Snow
No snow
(a) In the figure below, two secants are drawn to a circle from exterior point H.
Suppose that HZ=16.8, HX-14, and HY=42. Find HW.
H
w
M
HW = 0
(b) In the figure below, two chords intersect inside the circle at point V.
Suppose that VJ-18, VM-36, and VK=27. Find MN.
MN = 0
Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units; MN = 49.5 units.
How to Apply the Intersecting Secants and Chords Theorem?To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.
a. HZ * HW = HX * HY [based on the intersecting secants theorem]
Plug in the values:
16.8 * HW = 14 * 42
HW = 588/16.8
HW = 35 units
b. VK * VJ = VM * VN [based on the intersecting chords theorem]
Plug in the values:
27 * 18 = 36 * VN
VN = 486/36
VN = 13.5 units
MN = VM + VN = 36 + 13.5
MN = 49.5 units
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Consider a tech company that wants to offer free breakfast to its employees if their confidence interval shows it will decrease the
proportion of employees who skip breakfast.
Each interval shows the difference in proportion of p₁ - P2 where p₁ represents the employees who skip breakfast when free
breakfast is offered and p2 represents the employees who skip breakfast when free breakfast is not offered. Determine if there is
enough evidence to suggest that offering free breakfast results in an increase in the proportion of employees who don't skip
breakfast.
(-0.44,-0.16)
Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
Or
No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
(-0.25, 0.05)
Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
Or
No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
(-0.23, 0.15)
Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
Or
No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
Answer:
Step-by-step explanation:
In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.
Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.
For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.
Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.
So, the correct answer is:
For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.