I think of a number q, multiply it by 2 and add 5. I get the same answer as when I minus 2 from q. Find the value of q
Given:
A number is q, multiply it by 2 and add 5.
You get the same answer as when you minus 2 from q.
To find:
The value of q.
Solution:
The algebraic representation of the statement "a number is q, multiply it by 2 and add 5" is
Multiply q by 2 = 2q
Multiply q by 2 and then add 5 : 2q + 5
So, the first result is 2q+5.
When you minus 2 from q = q-2
So, the second result is q-2.
According to the question, both results are equal. Equate both results to get the value of q.
\(2q+5=q-2\)
Isolate variable terms.
\(2q-q=-5-2\)
\(q=-7\)
Therefore, the value of q is -7.
like the z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it. group startstrue or false
False. The statement is incorrect. Unlike the z distribution, the t-distribution is not symmetric around 0, and its tails do not approach the horizontal axis and cross it.
The t-distribution is similar to the normal (z) distribution in the sense that it is bell-shaped. However, there are important differences. The t-distribution is not symmetric around 0 but is centered at 0. It has a shape that depends on its degrees of freedom (df). As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution (z-distribution).
The tails of the t-distribution are thicker than the tails of the z-distribution. The t-distribution has more probability in the tails, which means it has more extreme values compared to the z-distribution. As the degrees of freedom increase, the t-distribution approaches the normal distribution, and its tails become closer to the horizontal axis, but they do not cross it.
It's important to note that the shape and characteristics of the t-distribution are determined by the degrees of freedom. As the degrees of freedom increase, the t-distribution becomes more similar to the z-distribution. However, even with large degrees of freedom, the t-distribution will always have slightly thicker tails than the z-distribution.
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Triangle ABC has coordinates A(1, 3), B(5, 6), and C(4, 8). 1.State the coordinates of A’B’C’, ABC after a 90 o counterclockwise rotation. [2 pts] 2.Plot the graph of A’B’C’. [2 pts] 3.State the coordinates of A”B”C”, A’B’C’ after a 180 o clockwise rotation. [2 pts] 4.Plot the graph of A”B”C”. [2 pts]
Answer:
66
77
u will do great u go guy
i rly need plz help so plz help :/
Answer:
Step-by-step explanation:
Follow PEMDAS
P = parenthasees
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
There are no P or E or M
so divide
-3 = h + 4
then we just subtract four on both sides
h = -7
An automatic machine in a manufacturing process is operating groperly if the iengths of an important subcomponent are normally distributed with a mean of izal cri and a otandard deviation of 5.6 cm. A. Find the probability that one selected subcomponent is longer than 122 cm, Probability = B3. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 122 cm. Probability win C. Find the probabilify that if 3 are randomly selected, ail 3 have lengths that exceed 122 cm. Probability =
A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.
z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)
Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.
B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.
The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.
Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm
Now we can calculate the z-score for a mean length of 122 cm:
z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)
Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.
C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.
Probability = (0.9999)^3 ≈ 0.9997
Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.
Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.
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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 411.0 gram setting. it is believed that the machine is underfilling the bags. a 35 bag sample had a mean of 406.0 grams. a level of significance of 0.05 will be used. state the hypotheses. assume the standard deviation is known to be 25.0.
Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.
To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.
Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)
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I remember all the boys used to like this one girl in 6th grade because she was already full developed and she had curly hair and a good face shape. But in 8th grade she ended up doing hardcore drûgs and smôking pot, and stopped showing up to school. And today I came across her inśtagram page and wow she really messed herself up she looks like somebody’s aunty who just got out of jail. And she ended up dropping out.
Answer:
Wow that's messed up and was she black or white
Ravi presses f12 (command shift s) and then clicks on the tools button. what is he doing?
He is opening a dialog box to access a second workbook by pressing F12 and then clicking tool box.
A dialog box is a temporary window an application creates to retrieve user input. An application typically uses dialog boxes to prompt the user for additional information for menu items.It (also spelled dialogue box, also called a dialog) is a common type of window in the GUI of an operating system. The dialog box displays additional information, and asks a user for input. For example, when you are using a program and you want to open a file, you interact with the "File Open" dialog box.
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which graph shows the solution to the system of linear equations?
y=-1/3x+1
y=-2x-3
y = -1/3x + 1
y = -2x - 3
We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.
The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.
The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.
Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.
Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.
Consider the statement: Subtract 28 from t and multiply the difference by 4.
Which expression represents the statement above?
A. 4(28*t)
B.t-28*4
C.28-t*4
D.4(t-28)
Answer:
D!
Step-by-step explanation:
We need to obviously subtract, only C and D do thatt. But, you don't multiple t or 28 by 4. You need to multiply the difference, so you need parentheses!
Omar invests £2800 for 3 years at 1.75% simple interest per year.
How much is the investment worth at the end of the 3 years?
Answer:
£2947
Step-by-step explanation:
the formula for simple interest is interest = prt.
p is the principal value, or what omar had at the beginning.
r is the rate at that you gain interest.
t is the amount of time in years.
so, plugging in our values, we multiply 2800*3*0.0175 to get 147.
now, since that was the amount of interest omar gained, we still have to add the original amount that he had, and 2800+147 = 2947.
so, the answer is £2947.
PLEASE HELP 15 POINTS! Which of the following can be used to rewrite the expression (3)(2+c)? There are two correct answers. A) Commutative Property of Multiplication B) Associative Property of Addition C) Associative Property of Multiplication D) Commutative Property of Addition
Answer:
A and D
Step-by-step explanation:
You can switch the orders of the two groups so that it is (2+c)(3) and you can switch the orders of 2 and c and neither would change the answer.
Algebraic math question
Answer:
\( 7 \: {ft}^{2} \)
Step-by-step explanation:
Area of the trapezoidal table
\( =\frac{1}{\cancel 2}(4 + 3)\times \cancel 2\)
\( = 7 \: {ft}^{2} \)
Answer:
7 ft squared
Step-by-step explanation:
Area of the trapezoidal table
What is the y-coordinate of the y-intercept of the parabola y=x^2+1
Answer:
-1/4 or -0.25
Step-by-step explanation:
use completing the square
hope this is right :)
Ben and Landon took turns driving on the recent 820 mile road trip Ben averaged 60 mph while Landon average 56 mph if the trip took them 14 hours how many hours did Landon Drive
Answer:
9 hours
Step-by-step explanation:
Let :
Landon hours = x
Ben hours = y
x + y = 14 - - (1)
60x + 56y = 820 - - - (2)
From (1)
y = 14 - x
60x + 56(14 - x) = 820
60x + 784 - 56x = 820
4x = 820 - 784
4x = 36
x = 36/4
x = 9
Landon drove for 9 hours
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x)= 1/x,[1,6] O Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. O Yes, f is continuous on [1,6] and differentiable on (1,6). O No, f is not continuous on [1,6]. O No, f is continuous on [1,6] but not differentiable on (1,6). O There is not enough information to verify if this function satisfies the Mean Value Theorem.
To determine if the function f(x) = 1/x satisfies the hypotheses of the Mean Value Theorem on the given interval [1,6], we need to check if the function is continuous on the interval and differentiable on the open interval (1,6).
In this case, f(x) = 1/x is continuous on the interval [1,6] because it is defined and continuous for all values of x within that interval.
However, f(x) = 1/x is not differentiable at x = 0 since the derivative is undefined at that point. But since the interval of interest is [1,6], which does not include x = 0, we only need to consider the differentiability of the function on the open interval (1,6).
On the open interval (1,6), f(x) = 1/x is differentiable because it is the reciprocal of a differentiable function, except at x = 0 which is not included in the interval (1,6).
Therefore, the function f(x) = 1/x satisfies the hypotheses of the Mean Value Theorem on the given interval [1,6] because it is continuous on [1,6] and differentiable on (1,6).
The correct answer is: O Yes, f is continuous on [1,6] and differentiable on (1,6).
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Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 5 ≤ x ≤9.
7
8
9
6
x
4
5
f(x)
4
8
16
32
64
medically explained PAINL X
128
Deltal/ath
The average rate of change, in simplest form, is -2/5.
What is average rate ?
Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.
The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
\(m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$\)
Using the coordinate points from the table (0,41) and (15,35)
Substitute the coordinate into the expression:
\($$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$\)
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Jack is mixing red paint with blue paint to make purple paint. he adds 2/5 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 2/15 fluid ounces of purple. how many fluid ounces of red paint will he need to make 5 fluid ounces of purple paint?
Answer:
Step-by-step explanation:
Change 2/5 to a decimal
2/5 = 0.4
Change 1 2/15 of a fluid ounce to a decimal.
1.133333
Set up your proportion.
0.4 / 1.133333 = x / 5 Cross multiply
0.4*5 = 1.133333*x
2 = 1.133333 x Divide by 1.1333333
2/1.33333 = x
x = 1.5 ounces.
He needs 1.5 ounces of red to make 5 ounces of purple.
Match each set of equations with the move that turned the first equation into the second. (You are telling me what happened from the first numbers to the second set of number in each pair)
Prompt 1-4(5x-7)=-18 --->5x-7=4.5
Answer for prompt 1 -4(5x-7)=-18 --->5x-7=4.5
Prompt 28-10x=7+5x --->4-10x=3+5x
Answer for prompt 2 8-10x=7+5x --->4-10x=3+5x
Prompt 36x+9=4x-3 --->2x+9=-3
Answer for prompt 3 6x+9=4x-3 --->2x+9=-3
Prompt 4-5x/4=-4 ---> 5x=-16
Answer for prompt 4 -5x/4=-4 ---> 5x=-16
The value of x from the expression is 2.3
What is an equation?Given the equation
-4(5x-7)=-18We are to get the value of x following the steps;
Given;
-4(5x-7)=-18ExpansionExpand the expression
-4(5x) -4(-7) = -18
-20x + 28 = -18
Subtract 18 from both sides
-20x + 28 - 28 = -18 - 28
-20x = -46
x = 2.3
Hence the value of x from the expression is 2.3
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What is the value of x
x=
According to the U.S Census Bureau publication Demographic Profiles, a relative frequency distribution of the U.S resident population by region in 2000 is as follows;
Region/ Rel freq, Northeast 0.190, Midwest 0.229, South 0.356, West 0.223.
At simple random sample of this years U. S residents gave the following frequency distribution;
Region/ Frequency, Northeast 50, Midwest 43, South 111, West 46
At the 5% significance level, do the date provide sufficient evidence to conclude that this year's resident population distribution by region has changed from the 2000 distribution?
We need to perform a chi-square goodness-of-fit test to determine if this year's U.S. resident population distribution by region has changed from the 2000 distribution at a 5% significance level.
The expected frequencies for each region can be calculated by multiplying the total sample size (250) by the relative frequency for each region in the 2000 distribution. For example, the expected frequency for the Northeast region is 250 * 0.190 = 47.5.
We can calculate the chi-square test statistic using the formula:
χ2 = ∑(observed frequency - expected frequency)2 / expected frequency
The degrees of freedom for this test is (number of regions - 1) = 3.
Using the given data and expected frequencies, we can calculate the test statistic to be χ2 = 4.729.
Using a chi-square distribution table with 3 degrees of freedom and a 5% significance level, the critical value is 7.815.
Since the calculated test statistic (4.729) is less than the critical value (7.815), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that this year's resident population distribution by region has changed from the 2000 distribution at a 5% significance level.
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Given the graph below, determine the values for a and b in the equation y=blog3(x+a). If a value is a non-integer then type it as a reduced fraction.
The values of b and a for the logarithmic function in this problem are given as follows:
a = -4.b = -2.1.How to define the logarithmic function?The logarithmic function in the context of this problem has the format given as follows:
\(y = b\log_3{x + a}\)
The vertical asymptote is at x = -4, hence:
\(y = b\log_3{x - 4}\)
When x = 5, y = -1, hence the parameter b is obtained as follows:
\(-1 = b\log_3{5 - 4}\)
0.477b = -1
b = -1/0.477
b = -2.1.
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Two sides of a triangle are 4m and 5m in length and the angle between them is increasing at a rate of 0.06rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of the fixed-length is π3
.
The rate at which the area of the triangle is increasing when the angle between the sides of the fixed-length is pi/3 is 0.15 square meters per second. To solve this problem, we need to use the formula for the area of a triangle: A = 1/2 * base * height. In this case, the base is the side of length 5m and the height is the perpendicular distance from that side to the other side.
Let's call the angle between the sides of length 4m and 5m "theta". We know that d(theta)/dt = 0.06 rad/sec. We want to find dA/dt when theta = pi/3.
First, we need to find the height of the triangle when theta = pi/3. To do this, we can use the sine function: sin(pi/3) = sqrt(3)/2. So the height of the triangle is h = 4m * sqrt(3)/2 = 2m * sqrt(3).
Now we can find dA/dt using the product rule and the chain rule:
dA/dt = (1/2) * (d/dt)(5m) * h + (1/2) * 5m * (d/dt)(h)
The first term is 0 because the length of the base is fixed at 5m. The second term is:
dA/dt = (1/2) * 5m * (d/dt)(2m*sqrt(3))
= 5m * sqrt(3) * (d/dt)(sqrt(3))
= 5m * sqrt(3) * (1/2)*(d/dt)(theta)
= 5m * sqrt(3) * (1/2)*0.06 rad/sec
= 0.15m^2/sec
Therefore, the rate at which the area of the triangle is increasing when the angle between the sides of the fixed-length is pi/3 is 0.15 square meters per second.
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what must be your average speed in order to travel 350 km in 5.15 h?
Answer:
68 km/h--------------
Average speed equation:
s = d/t, where d- total distance, t - total timeSubstitute 350 for d and 5.15 for t:
s = 350/5.15s = 67.96 ≈ 68 km/hThe average speed must be approximately 68 km per hour.
what is the surface area
The surface area of the figure would be 5 cm².
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
Given is a 2 - D figure as shown in the image.
We can write the surface area as -
{S} = A{cube} + 4 x A{triangle}
{S} = (1 x 1) + (4 x 1/2 x 1 x 2)
{S} = 1 + 4
{S} = 5 cm²
Therefore, the surface area of the figure would be 5 cm².
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The triangle below has been reduced by a scale of 0.4. 10 cm
30 cm
↓
[Not drawn to scale]
What is the area of the reduced triangle?
Answer:
To find the area of the reduced triangle, we need to know the length of the base and the height of the triangle after the scaling.
Since the triangle has been reduced by a scale of 0.4, the length of each side has been multiplied by 0.4. Therefore, the base of the reduced triangle is:
10 cm × 0.4 = 4 cm
To find the height of the reduced triangle, we can use the fact that the ratio of corresponding sides in similar triangles is the same. Since the triangle has been scaled down by a factor of 0.4, the ratio of the corresponding sides is 0.4. Therefore, the height of the reduced triangle is:
30 cm × 0.4 = 12 cm
Now that we know the base and the height of the reduced triangle, we can calculate its area using the formula:
Area = (1/2) × base × height
Area = (1/2) × 4 cm × 12 cm
Area = 24 cm²
Therefore, the area of the reduced triangle is 24 cm².
Step-by-step explanation:
red.
46
43
52
114 116
25 Cf + on
98
-
Pd
Reset
Tc
Next
DELL
Cf
136 Te+
52
+ 3 n
The measure of arc CF is 148 degrees from the figure.
The external angle at E is half the difference of the measures of arcs FD and FC.
We have to find the measure of arc CF.
∠CEF = 1/2(arc CF - arc DF)
52=1/2(x-44)
Distribute 1/2 on the right hand side of the equation:
52=1/2x-1/2(44)
52=1/2x-22
Add 22 on both sides:
52+22=1/2x
74=1/2x
x=2×74
x=148
Hence, the measure of arc CF is 148 degrees.
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Dina invests £450 in a savings account with annual compound interest.
After five years, there is £534.46 in the account.
What interest rate has she been receiving?
Answer:
3.3%
Step-by-step explanation:
compound interest: A = Pe^(rt)
A = 534.46
P = 450
t = 5
534.46/450 = e^(5r)
e^(5r) = 1.18
lne^(5r) = ln 1.18
(5r)lne = ln1.18
ln1.18 = 5r
5r = 0.165
r = 0.033
or 3.3%
Find three consecutive odd integers such that three times the greatest is 7 less than the
sum of the smallest and middle integer.
Consecutive odd integers are odd integers that have a difference of 2
The consecutive integers are -17, -15 and -13
How to determine the integersLet the integers be x, y and z (from least to greatest)
So, we have:
\(3z =x + y - 7\)
Also, we have:
\(y = x + 2\)
\(z = x + 4\)
So, we have:
\(3z =x + y - 7\)
\(3(x + 4) = x + x + 2 - 7\)
Open the bracket
\(3x + 12 = x + x + 2 - 7\)
Collect like terms
\(3x -x -x = 2 - 7-12\)
\(x = -17\)
Hence, the consecutive integers are -17, -15 and -13
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Write a 5 digit number so that when you round to the nearest hundredth, your answer is 14.6. The number cannot include any zeros.
Answer:
14.598
Step-by-step explanation:
When you round that number to the nearest hundredth, you'll get 14.6. Hope this helps.