Step-by-step explanation:
Pick two convenient points to calculate the slope, m
I'll use (2.5,80) and (5.5, 95)
m = slope = (y1-y2)/(x1-x2) = (80 - 95) / ( 2.5 - 5.5 ) = -15 / -3 = 5
Slope intercept form of a line is y = mx = b
y = 5x + b Use one of the points to calculate 'b'
95 = 5 (5.5) + b shows b = 67.5
Line equation is then:
y = 5x + 67.5
Find the value of cos
X
X rounded to the nearest hundredth, if necessary.
Please help fast
Answer:
\(\cos(x) \approx 0.82\)
Step-by-step explanation:
Cosine is defined as:
adjacent / hypotenuse.
We can determine that 18 is the side adjacent to x, and that 22 is the triangle's hypotenuse.
Putting these values into the definition of cosine:
\(\cos(x) = \dfrac{\text{adj}}{\text{hyp}}\)
\(\cos(x) = \dfrac{18}{22}\)
\(\cos(x) \approx 0.82\)
Answer:
cos x= adjacent/hypotenus
cos x= 18/22
cos x=0.8182
x=35.09⁰
select all the values of x that make the inequality true. x < -4.8
Please respond ASAP
Answer:
4.8
Step-by-step explanation:
i think
Marcella has an empty pyramid shaped container and an empty prison shaped container. the base of the pyramid is congruent to the base of the prism, and their heights are equal. how many times must marcella fill the pyramid with water and pour it into the prism in order to completely filled the prison with water
Marcella must fill the pyramid with water and pour it into the prism three times in order to completely fill the prism with water.
In this question, we have a pyramid-shaped container and a prism-shaped container. It is given that the base of the pyramid is congruent to the base of the prism, and their heights are equal. We need to find how many times Marcella must fill the pyramid with water and pour it into the prism in order to completely fill the prism with water.Let the volume of the pyramid-shaped container be P and the volume of the prism-shaped container be R. Since the base of the pyramid is congruent to the base of the prism, their base areas are equal. Let this base area be A.
Therefore, we have:
Volume of the pyramid = (1/3) × A × h Volume of the prism = A × h where h is the height of both containers.
Since the heights of the pyramid and prism are equal, we can cancel them out from the above equations. Hence, we have:
Volume of the pyramid = (1/3) × A × h Volume of the prism = A × h Volume of the prism/Volume of the pyramid = 3
This means that the volume of the prism is three times the volume of the pyramid.
Therefore, Marcella must fill the pyramid with water and pour it into the prism three times in order to completely fill the prism with water.
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In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculate the 95% confidence interval for the proportion of students who get coaching on the SAT .
Answer:
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
427 had paid for coaching courses and the remaining 2733 had not.
This means that \(n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351\)
95% confidence level
So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).
The lower limit of this interval is:
\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232\)
The upper limit of this interval is:
\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147\)
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
Urgent!! Math work in image!! Urgent help!!
The TV would not fit as the TV is too tall option (C) is correct after applying the concept of the ratio.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The aspect ratio is:
= 4:3
Multiply by 16 to the above ratio:
= 64: 48
The height in the area = 47"
But from the aspect ratio the height of the TV = 48"
Thus, the TV would not fit as the TV is a too tall option (C) is correct after applying the concept of the ratio.
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21.5% of 825 is
what number?
Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = −1, g(1) = −2, and g'(1) = 3. Find h'(1). h(x) = (x2 + 8)g(x)
Answer:
\(h'(1) = 23\)
Step-by-step explanation:
Let be \(h(x) = (x^{2}+8)\cdot g(x)\), where \(r(x) = x^{2} + 8\). If both \(r(x)\) and \(g(x)\) are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:
\(h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)\)
\(r'(x) = 2\cdot x\)
\(h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)\)
Given that \(x = 1\), \(g (1) = -2\) and \(g'(1) = 3\), the derivative of \(h(x)\) evaluated in \(x = 1\) is:
\(h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)\)
\(h'(1) = 23\)
当 1. Resuelas las seguintes multiplicación y divisiones (-5,55 ÷ 0,25)x (2,85)
Answer:
uno=dose
Step-by-step explanation:
....................
Answer:
10.7%
Step-by-step explanation:
Hope this helps :)
8. What is the value of x in the diagram?
A
E
429
B
49
D
32°C
Answer:
D. \(10^{\circ}\)
Step-by-step explanation:
Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).
Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).
By the inscribed angle theorem, \(\alpha=84^{\circ}\).
Thus, \(\beta=20^{\circ}\).
By the inscribed angle theorem, \(x=10^{\circ}\).
Multiply.
3√2•2√8•√3•√6
Enter your answer, in simplest radical form, in the box.
The simple radical form is 72√2.
What is simple radical form?
If we know the prime factorization of 32, we can write the simplest radical form of the square root of 32. Thus, the prime factorization of 32 is 2 × 2 × 2 × 2 × 2. If it is written in the radical form, then the simplest radical form of the square root of 32 is 4√2. Square Root of 32 in Radical Form: 4√2.
Given,
3√2•2√8•√3•√6
= 3×√2×2×√8×√3×√6
as we know √ab = √a√b
we can write, √8 = √2√4 and √6 =√2√3
we get,
=3×√2×√2×√4×√3×√3×√2
=3×2×2×3×√2
=72√2
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Please HELP!!!
Will give 15 points!!
For a test that’s due today!!
Answer:
A
Step-by-step explanation:
For a right triangle
\(A=\frac{ab}{2} \\\frac{(10.4)(15.3)}{2} =79.56\)
This is the same as the other triangle because they are the same size because of congruency
Area of the rectangle
\(a^2+b^2=c^2\\\)
\(\sqrt{(10.4^2+15.3^2} =c\)
\(c= 18.5\)
18.5 x 7 = 129.5
Add them all up
129.5+79.56+79.56= 288.62
Find the range of f(-5)=-2|x-5|+8 please with explination.
Answer:
Domain: set of possible input values (x-values)
Range: set of output values (y-values)
The range for the function \(f(x)=-2|x-5|+8\) is:
\(f(x)\leq 8\)
(5, 8) is the vertex of the line
Because |x - 5| is absolute (so always positive) and it is multiplied by -2,
-2|x - 5| will always be negative unless x = 5 (when it will be zero). Therefore, the max y-value is 8.
However, your question actually asked what the function is when x = -5:
\(f(-5)=-2|x-5|+8\\\\= -2|-5-5|+8\\\\= -12\)
Step-by-step explanation:
Thats the all rhe answers step by step
What’s the quotient ? I’m helping out with my sisters homework once again and I don’t wanna explain it to her. Please help me ;-;
Answer:
quotient is the answer to division. So if 7/2=3 with a remainder of 1, then the quotient is 3
11/12 x 6/11 in simplest form
1a. [1 mark] Jim heated a liquid until it boiled. He measured the temperature of the liquid as it cooled. The
following table shows its temperature, d degrees Celsius, t minutes after it boiled.
r (min)
0
4
8
12
16
20
d (°C)
105
98.4
85.4
74.8
68.7
62.1
Write down the independent variable
The independent variable is time.
What is independent variable?An independent variable is a variable that represents a quantity that is being manipulated in an experiment. x is often the variable used to represent the independent variable in an equation.
Given:
r (min) d (°C)
0 105
4 98.4
8 85.4
12 74.8
16 68.7
20 62.1
As, from the table it can be seen that the temperature vary in accordance with time but the time isn't depend on any variable.
Hence, the independent variable is time.
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How much of a circle does a 100-degree angle turn through? The answers for the question are 1, 100/180, 50/360, and 100/360. Which one is right?
Answer:
D
Step-by-step explanation:
The answer is D because a circle has at least a 360 degree and a 180 is a half circle.
Simplify by combining like terms.
11y+ 7y 3y² – 4y²
Answer:
\(21y^{3} - 4y^{2} + 11y\)
Step-by-step explanation:
\(11y + 7y(3)y^{2} - 4y^{2}\)
=11y + 21y^3 +-4y^2
\(=21y^{3}-4y^{2}+11y\)
Find the value of y for the given value of x.
y=2−9x;x=2/3
Answer:
-4
Step-by-step explanation:
y=2-9×(2/3)=2-6= -4
Write a function rule for
Answer:
x^2
Step-by-step explanation:
1^2=1
2^2=4
3^2=9
Jamie wants a new smart TV/sound system that costs $1,250. He does not have that much in cash to purchase it, so he uses a credit card with 18% annual interest. He puts $250 down, but he only pays the interest each month on that credit card debt. About how much will he pay in interest over 4 years?
Jamie would pay $720 in interest in 4 years
The amount of interest he would have to pay = amount borrowed x interest rate x time
Amount borrowed = cost of the TV - amount put down
$1250 - $250 = $1000
Interest rate = 18%
Time = 4 years
Interest = 1000 x 0.18 x 4 = $720
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Interest is indeed the loan cost, in which the borrower pays this same lender a fee for the loan. Income is either simple or compounded, typically expressed in percentage. In this, the interest is $720, that's calculation can be defined as follows:
Given:
Rate of Interest \(= 18\%\)Time = 4 yearsUsing Formula:
\(\to \bold{\text{Interest =amount borrowed}}\times \bold{\text{interest rate}}\times \bold{\text{time}}\\\\\to \bold{\text{Borrowed amount = Television cost}} - \bold{\text{amount proclaimed}}\)
Calculating Borrowed amount:
\(\text{} =\$1250 - \$250 =\$1000\)
Calculating Interest:
\(\bold{= 1000 \times 18\% \times 4} \\\\\bold{= 1000 \times \frac{18}{100} \times 4} \\\\\bold{= 10 \times 18 \times 4} \\\\\bold{=\$ 720}\)
Therefore, In 4 years Jamie would pay $720 as interest.
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Misty’s surgery lasted 214 hours. Convert the time to seconds.
Answer:
770,400
Step-by-step explanation:
770,400 seconds
A Factor with the distributive property Apply the distributive property to factor out the greatest common factor, 56+32 Stuck? Watch a video or use a hint.
the greatest commmon factor of 56 and 32 is 8
so in order to use the distributive property
8(7+4)=56+32=88
Where are the minimum and maximum values for f(x)A. min: x =2¹ 2Reset Selectionmax:z = = 0, π, 2πOB. min:z = π max:x = 0, 2OC. min:z = 0, 2π max:x = πOD. min:z = ,,max:x = 0, 3, 4,2=- 3 cos z - 2 on the interval [0, 2π]?2P
Given:
The function f(x) = 3cos(x) - 2.
Required:
What are the minimum and maximum value of function?
Explanation:
To check maximum and minimum value of function.
First derivate the original function.
After putting first derivative equal to zero, critical points can be found.
Then, do second deritvative to check points of maxima and minima.
The critical points at which second derivative greater than zero. Point will be of minima.
The critical points at which second derivative less than zero. Point will be of maxima.
So,
\(\begin{gathered} f(x)=3cos(x)-2 \\ \text{ First derivative} \\ f^{\prime}(x)=-3sinx \\ \text{ Put }f^{\prime}(x)=0 \\ sinx=0 \\ x=0,\pi,2\pi \end{gathered}\)Now, do second derivative test for maximum and minimum points
\(\begin{gathered} f^{\prime}^{\prime}(x)=-3cosx \\ \text{ At }x=0 \\ f^{\prime}^{\prime}(0)=-3\times1=-3<0 \\ \text{ At }x=\pi \\ f^{\prime}^{\prime}(\pi)=-3\times cos(\pi)=-3\times-1=3>0 \\ At\text{ }x=2\pi \\ f^{\prime}^{\prime}(2\pi)=-3\times1=-3<0 \\ \end{gathered}\)Answer:
\(\text{ The points }0,2\pi\text{ are points of maxima and }\pi\text{ giving minima.}\)
Lois and her team used the number of red candies in a
small 9 ounce bag to predict the number of red candies in
a large 33 ounce bag. If Lois counted 12 red candies in the
small bag, Predict the number of red candies in the large bag.
Use proportional reasoning and show algebraic work.
Using proportional reasoning, we can predict that there will be 40 red candies in the large bag.
Using proportional reasoning, we can set up and solve the following equation to determine the number of red candies in the large bag:
P = Proportion of red candies in the large bag
R = Red candies in the small bag
R × (33/9) = P
12 × (33/9) = P
P = 40 red candies in the large bag
Therefore, using proportional reasoning, we can predict that there will be 40 red candies in the large bag.
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Tickets for a dance recital cost $12 for adults and $8 for children. The dance company sold
257 tickets, and the total receipts were $2,576. How many adult tickets and how many child
tickets were sold? Set up a system of equations, state both variables, and solve. Write your
answer in a complete sentence and make sure to write the units.
Answer:
Step-by-step explanation:
a + c = 257
12a + 8c = 2576
-12a - 12c = -3084
12a + 8c = 2576
-4c = -508
c = 127 children tickets
a + 127 = 257
a = 130 adult tickets
PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
A regular polygon has 12 sides. If one of its angles measures (8h − 30)°, what is the value of h?
h = 10.75
h = 18.75
h = 20.25
h = 22.5
Answer: h = 22.5
Step-by-step explanation:
Total angle area of a 12 sided polygon is 1800
1. One angle would be 1800/12= 150
8h - 30 = 1502. Add 30 one each side to cancel out and only leave 8h.
8h = 1803. To get rid of the 8 we divide the the other side by 8.
h = 22.5The answer is 22.5
Answer: D 22.5 i got it right on the exam
Step-by-step explanation:
answer asap :)
In parallelogram ABCD ABCD, ∠D=125°. What is ∠B?
Step-by-step explanation:
the answer is
<B = <D
<B = 125°
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.
a. What is the probability that a student scored below 91 on this exam?
b. What is the probability that a student scored between 65 and 89?
c. If the professor grades on a curve (i.e., gives A’s to the top 10% of the class, regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam, where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain. (Hint: For option 1, you need to find a minimum Z-score that will guarantee you that you will be in the top 10% of the class.)
a. The probability that a student scored below 91 on this exam is 0.9878
b. The probability that a student scored between 65 and 89 is 0.8186.
c. A grade of 68 on the second exam is better than a grade of 81 on the first exam for the given conditions
a. To find the probability that a student scored below 91 on the exam, we need to find the area under the normal distribution curve to the left of 91. Using a standard normal distribution table or calculator, we can find the corresponding Z-score as:
Z = (91 - 73) / 8 = 2.25
The probability of scoring below 91 is then the same as the probability of a standard normal random variable being less than 2.25, which is approximately 0.9878.
b. To find the probability that a student scored between 65 and 89, we need to find the area under the normal distribution curve between these two values. Using the Z-score formula as above, we find:
Z1 = (65 - 73) / 8 = -1.00
Z2 = (89 - 73) / 8 = 2.00
Using a standard normal distribution table or calculator, we can find the probability of a standard normal random variable being between -1.00 and 2.00, which is approximately 0.8186.
c. To determine if a grade of 81 on this exam or a grade of 68 on a different exam is better if the professor grades on a curve, we need to find the Z-score that corresponds to the top 10% of the class. Using a standard normal distribution table or calculator, we can find this Z-score as:
Z = 1.28 (approximately)
For the first exam, the Z-score corresponding to a grade of 81 is:
Z = (81 - 73) / 8 = 1.00
Since 1.00 < 1.28, a grade of 81 is not in the top 10% of the class. For the second exam, the Z-score corresponding to a grade of 68 is:
Z = (68 - 62) / 3 = 2.00
Since 2.00 > 1.28, a grade of 68 is in the top 10% of the class. Therefore, if the professor grades on a curve, a grade of 68 on the second exam is better than a grade of 81 on the first exam.
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if angle poa is a right angle and if measure of angle coa is three times as large as measure angle poc.
The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.
POA is a right angle so it is 90 degrees.
POC +COA = 90 .....(1)
Also, POC is 3 times as large as COA.
Let's take COA, "x"
POC = 3x
Substituting the values in equation (1) as follows:
x + 3x = 90
4x = 90
x= 22.5
Therefore,
COA = 22.5°
POC = 22.5*3 = 67.5°
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