Samuel runs 5 meters per second best describes the slope of the linear equation
Given that Samuel runs around a 100 meter track.
He uses the linear equation y=200+5x to describe how far he runs after he has already jogged two laps.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
y=200+5x
y=5x+200
Slope is 5
Hence, Samuel runs 5 meters per second best describes the slope of the linear equation
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ1
NO LINKS!! URGENT HELP PLEASE!!!!
Find the equation of square root with a vertex at (1, -5) and passes through the (5, -7).
Answer:
[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]
Step-by-step explanation:
The standard equation of a square root function with vertex at point (h,k) is given by:
[tex]y = a \times \sqrt{x - h} + k[/tex]
where (h,k) is the vertex and "a" is a coefficient that determines the vertical stretch and direction of the square root function.
We know that the vertex of our square root function is (1, -5), so we can substitute those values into the equation to get:
y = [tex] a*\sqrt{x-1} - 5[/tex]
Now, we need to find the value of "a". To do that, we will use the fact that the square root function passes through point (5, -7). Substituting these coordinates into the equation, we get:
[tex]-7 = a*\sqrt(5-1) - 5[/tex]
-2 = 4a
[tex]a = \frac{ - 1}{2} [/tex]
Now that we know the value of "a", we can substitute it into our equation to get the final equation of the square root function:
[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]
Therefore, the equation of the square root function with a vertex at (1, -5) and passing through (5, -7) is
[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]
Answer:
[tex]f(x) = -\sqrt{x-1} - 5[/tex]
Step-by-step explanation:
The standard form of a square root function is:
[tex]f(x)=a\sqrt{x-h}+k[/tex]
where "a" is a scaling factor determining the vertical stretch or compression of the function, and (h, k) is the vertex.
Given the vertex is (1, -5), substitute h = 1 and k = -5 into the equation:
[tex]f(x) = a\sqrt{x - 1} - 5[/tex]
Substitute the point (5, -7) that the function passes through to find the stretch factor "a":
[tex]\begin{aligned}-7 &= a \sqrt{5 - 1} - 5\\-7 &= a \sqrt{4} - 5\\-7 &= 2a - 5\\-7 +5&= 2a - 5+5\\-2&= 2a\\\dfrac{-2}{2}&=\dfrac{2a}{2}\\-1&=a\\a &= -1\end{aligned}[/tex]
Substitute the value of "a" back into the equation:
[tex]f(x) = -\sqrt{x-1} - 5[/tex]
Therefore, the equation of the square root function with a vertex at (1, -5) and passes through the point (5, -7) is:
[tex]\boxed{f(x) = -\sqrt{x-1} - 5}[/tex]
What transformations take the graph of f(x) = e^x to f(x) = -e^x -2?
The transformations of the given functions is vertical shift 2 units down.
Given that, the function is f(x)=-eˣ to f(x)=-eˣ-2.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function: f(x)= −eˣ
Horizontal Shift: None
Vertical Shift: Down 2 Units
Reflection about the x-axis: None
Vertical Compression or Stretch: None
Therefore, the transformations of the given functions is vertical shift 2 units down.
Learn more about the transformation here:
https://brainly.com/question/11709244.
#SPJ1
Can someone help with this?
Answer: the real zero of this equation is 5/3.
Please help me out! :D
Answer:
A
Step-by-step explanation:
Gwen has $50 in a savings account that earns 5% annually. The interest is not compounded. How many years will it take for her to have $57.50 in her
account?
Answer:
3 years
Step-by-step explanation:
1. Find 5 percent of 50.
5 percent of 50 is 2.5.
However, we are talking about money so we will say 2.50.
2. Add to 50 until you reach your desired number.
50 + 2.50 = 52.50
52.50 +2.50 = 55
55+2.50 = 57.50
Finally we have reached 57.50. It took us 3 equations to get there and therefore took 3 years.
please help!! use the job salaries to caculate each question :)
The profession that would earn that amount more than a bank teller is Office Clerk.
The profession that would earn $1,151,700 in 30 years is Bookkeeper.
The profession that will earn $828,600 over a 20-year career is Truck Driver.
The profession that earns $136,200 more than a fire fighter over a period of 30 years is Electrician
How to find the careers ?The 15 year difference between bank teller and office clerk is:
= ( 30, 850 x 15 ) - ( 27, 260 x 15 )
= $ 53, 850
The earnings of a Bookkeeper in 30 years is:
= 38, 390 x 30
= $ 1, 151, 700
The earnings of a Truck driver in 20 years is :
= 41, 430 x 20
= $ 828, 600
The difference between earnings of Fire fighter and Electrician over 30 years is:
= ( 52, 570 x 30 ) - ( 48, 030 x 30 )
= $ 136, 200
Find out more on earnings at https://brainly.com/question/30981057
#SPJ1
A closet in Shivani's house is 2 yards by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $38.00 per square yard?
The amount it would cost to put a new floor in the closet is $76.00
Calculating how much it would cost to put a new floor in the closetFrom the question, we are to calculate how much it would cost to put a new floor in the closet
From the given information,
A closet in the house is 2 yards by 1 yard.
To determine how much it would cost to put a new floor in the closet,
First,
We calculate the area of the closet
Area of the closet = 2 yard × 1 yard
Area of the closet = 2 square yards
Now,
From the given information,
The flooring costs $38.00 per square yard
Thus,
The amount it would cost to put a new floor in the closet is
2 × $38.00
= $76.00
Hence,
The amount it would cost is $76.00
Learn more on Calculating cost here: https://brainly.com/question/1662561
#SPJ1
Given that the triangles shown below are similar, what is the value of x?
ܐ ܠ ܐ
H
48
40
16
20
What is the area of the triangle?
3 cm
9 cm
8 cm
square centimeters
The measure of weights of 15 students is normally distributed with a sample mean of 6 and standard deviation of 5. Find the 95% confidence interval for the mean.
The 95% confidence interval for the mean is [3.23, 8.76].
What is the confidence of interval?
The confidence of interval of the mean is calculated as follows;
Confidence interval = σ ± (t-value x μ)
where;
σ is the sample meanμ is the standard errorThe standard error is calculated as follows:
μ = std / √n
μ = 5 / √15
μ = 1.29
Based on this value we will check the distrbution table, for the t-value of 95% confidence;
= 2.145.
Confidence interval = σ ± (t-value x μ)
= 6 ± (2.145 x 1.29)
= [3.23, 8.76]
Learn more about confidence interval here: https://brainly.com/question/20309162
#SPJ1
In 2009 the world’s largest pumpkin weighed 784 kilograms. An average-sized pumpkin weights 5,000 grams. The 2009 world record pumpkin weighs___ kilograms more than and average sized pumpkin. Write your answer as a numeral.
Step-by-step explanation:
5 000 gm = 5 kg
784kg - 5kg= 779 kg more than average
(x)<0 over and what other interval?
The other interval is (-1.1, 0.9)
In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.
For the given graph, values of f(x) are less than zero.
That means interval in which the values of the function are negative for the different values of x.
Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).
Therefore, from the given options, Option (4) will be the answer.
Learn more about intervals, click;
https://brainly.com/question/30486507
#SPJ1
The complete question is
F(x)<0 over (-∞, -3) and what other interval?
O (-2.4, - 1.1)
O (-3, - 1.1)
O (-1.1, 2)
O (-1.1, 0.9)
Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People
with fewer than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official
in Jordan suspects that Jordanian children are at risk of anemia. He measures a random sample of 50
children in Jordan and finds the mean to be 11.3 g/dl with a standard deviation of 1.6 g/dl. Test this
claim at the α = 0.05 level of significance.
Work this problem using both the p-value method OR the rejection region method.
There is enough data to indicate that Jordanian children are at risk of anemia.
The null hypothesis is that the true mean hemoglobin level for Jordanian children is greater than or equal to 12 g/dl, and the alternative hypothesis is that it is less than 12 g/dl.
Using the P-value method:
The test statistic for the one-sample t-test is given by:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population means (here, μ = 12), s is the sample standard deviation, and n is the sample size.
Substitute the given values,
t = (11.3 - 12) / (1.6 / √50) = -2.98
Using a t-distribution table with 49 degrees of freedom (df = n - 1), find that the p-value for this test is approximately 0.002.
Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that Jordanian children are at risk of anemia.
Learn more about the t-test here :
https://brainly.com/question/16945464
#SPJ1
Maria is creating a new art piece on canvas. (The canvas is represented in the picture below as
rectangle ARTS). She knows the base edge of the canvas, ST, measures 4 ft. And the distance of
diagonal AT measures 8.5 ft. What is the area of Maria’s canvas? Show all work.
The Area of Maria's canvas is 30 ft.
Area of Maria's canvas, we need to know the length of the other side of the rectangle. We can use the Pythagorean theorem to find this length. Let's call it SA.
According to the problem statement, the base edge ST measures 4 ft, and the diagonal AT measures 8.5 ft. Using the Pythagorean theorem, we have:
[tex]AT^2 = ST^2 + SA^2\\8.5^2 = 4^2 + SA^2\\72.25 = 16 + SA^2\\56.25 = SA^2\\SA = \sqrt{56.25}\\SA = 7.5\ ft[/tex]
Now we know that the length of the canvas is 7.5 ft, and the width is 4 ft. Therefore, the area of Maria's canvas is:
Area = length x width
Area = 7.5 ft x 4 ft
Area = 30 square feet
Therefore, the area of Maria's canvas is 30 square feet.
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
Students are making lemonade from a powdered lemon drink mix. Tristan mixes 7 cups of water and 3 cups of powdered lemon mix. Yaritza mixes 2 cups of water and 1 cup of powdered lemon mix. Use Tristan and Yaritza’s percent of water to determine whose mix will be more watery.
Comparing the percent of water, we can see that Tristan's mix has a higher percent of water, which means it will be more watery so Tristan's mix will be more watery than Yaritza's mix.
To determine whose mix will be more watery, we need to compare the percent of water in each mix.
The higher the percent of water, the more watery the mix will be.
Tristan's mix has a total of 7 + 3 = 10 cups of liquid
The percent of water in Tristan's mix is: (7 cups of water / 10 cups of liquid) x 100% = 70%
Yaritza's mix has a total of 2 + 1 = 3 cups of liquid (water + powdered lemon mix).
The percent of water in Yaritza's mix is: (2 cups of water / 3 cups of liquid) x 100% = 66.7%
Comparing the percent of water, we can see that Tristan's mix has a higher percent of water, which means it will be more watery.
Therefore, Tristan's mix will be more watery than Yaritza's mix.
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ1
Talk about an experience outside of academia where you had to assess and make a decision that came with risk. Please limit your response to 250 words or less.
An experience that I had outside the academia was when I worked as a marketing coordinator for a small start-up company.
What was the experience?A product launch event had been planned by the team for several weeks, and everything appeared to be going according to plan. However, we learned the day before the event that our keynote speaker, who was an important component of it, had unexpectedly become unwell and would not be able to attend.
I had to evaluate the situation as the marketing coordinator and decide right away. Either we could cancel the event or we could locate a another speaker.
Learn more about academia:https://brainly.com/question/30146443
#SPJ1
(2/5)y-5=-2.5
What's y
Answer: Y = 6.5
Step-by-step explanation:
Which of the following ratios would form a proportion with Two-thirds?
a.
Three-fourths
c.
StartFraction 12 Over 15 EndFraction
b.
StartFraction 6 Over 9 EndFraction
d.
One-third
The proportion equivalent with Two-thirds would be 6/9.
Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the proportion with Two-thirds
If you actually divide it’ll make since , so first we want to divide the 2 , then you want to multiply the third of the two
2/3 x 3/3
6/9
thus, the answer will be 6/9.
More can be learned about proportions at;
brainly.com/question/24372153
#SPJ1
answer with explanation
Answer:
Step-by-step explanation:
To create a magic square with -6,-5,-4,-3,-2,-1,1,2, we need to arrange these numbers in a 3x3 grid such that each row, column, and diagonal add up to the same sum.
Here's one possible solution:
diff
Copy code
-6 1 2
-4 -5 9
8 -3 -2
To check if this is a magic square, we can calculate the sum of each row, column, and diagonal:
Rows:
(-6 + 1 + 2) = -3
(-4 - 5 + 9) = 0
(8 - 3 - 2) = 3
Columns:
(-6 - 4 + 8) = -2
(1 - 5 - 3) = -7
(2 + 9 - 2) = 9
Diagonals:
(-6 - 5 - 2) = -13
(2 - 5 + 8) = 5
All of these sums are equal to 0, so this is indeed a magic square.
Garnier's Opera House is a revival of the________style.
Romantic
Gothic
Renaissance
Baroque
Answer: Garnier's Opera House is a revival of the Baroque style.
Find the maximum value of C=4x+2y subject to the following restraints x>2 x<5 y>1 y<6
The required maximum value of C is 16, and it occurs when x = 3 and y = 2.
To find the maximum value of C = 4x + 2y subject to the restraints x > 2, x < 5, y > 1, and y < 6, we can use the method of Lagrange multipliers.
First, we set up the Lagrangian function L as follows:
L = 4x + 2y - λ₁(x - 2) - λ₂(x - 5) - λ₃(y - 1) - λ₄(y - 6)
where λ1, λ2, λ3, and λ4 are Lagrange multipliers.
Next, we take the partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4, and set them equal to zero:
∂L/∂x = 4 - λ₁ - λ₂ = 0
∂L/∂y = 2 - λ₃ - λ = 0
∂L/∂λ₁ = x - 2 = 0
∂L/∂λ₁ = 5 - x = 0
∂L/∂λ₃ = y - 1 = 0
∂L/∂λ₄ = 6 - y = 0
Solving these equations simultaneously, we get:
λ₁ = 1, λ₂ = 3, λ₃ = 1, λ₄ = 1, x = 3, y = 2
Therefore, the maximum value of C is:
C = 4x + 2y = 4(3) + 2(2) = 16
So, the maximum value of C is 16, and it occurs when x = 3 and y = 2.
Learn more about Lagrange multipliers here:
https://brainly.com/question/30776684
#SPJ1
the picture to my math problem i posted before
a) From Carmen's results, the experimental probability of landing on black is given as follows: 6/25.
b) The theoretical probability of landing on black is given as follows: 1/5.
c) The correct statement is the second statement, as the number of trials increases, the two probabilities get closer.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
In 25 trials, 6 resulted in black, hence the experimental probability is given as follows:
p = 6/25.
Two out of 10 regions of the spinner are black, hence the theoretical probability is given as follows:
p = 2/10 = 1/5.
Missing InformationThe problem is given by the image presented at the end of the answer.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
solve for x
2x^2/3+9x^1/3= -4
The solution of the equation is x=0.08813 or 3.90664.
We have,
2x² / 3 + 9[tex]x^{1/3[/tex] = -4
Now, solving the equation for x
2x² + 27[tex]x^{1/3[/tex] = -12
Now, taking cube on both side we get
(2x² + 27[tex]x^{1/3[/tex] )³= -12³
Now, simplifying we get
19683x = -1728 -864x² -144[tex]x^4[/tex]-8[tex]x^6[/tex]
So, x=0.08813 or 3.90664
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ1
In Martha's food storage, she has 13 cans of chicken noodle soup, 15 cans of tomato soup, and 17 cans of mushroom soup. If she randomly chooses a can of soup from her food storage, what is the probability it is a can of tomato soup?
Answer:
1/3
Step-by-step explanation:
p(event) = (number of desired outcomes)/(total number of outcomes)
total number of outcomes = 13 + 15 + 17 = 45
number of desired outcomes = 15
p(can of tomato soup) = 15/45 = 1/3
Need some help I’m stuck
Below are the true and false results for the number sentence;
1. 6x = 48 when x = 6 is false
2. 6x = 48 when x = 8 is True
3. x/2 ≥ 3 when x = 6 is True
4. x/2 ≥ 3 when x = 8 is True
5. x < 8 when x = 6 is true
6. x < 8 when x = 8 is False
7. 5x ≤ 30 when x = 6 is True
8. 5x ≤ 30 when x = 8 is False
How do we solve for the number sentences?The solution to the number sentence are;
1. 6 x 6 = 36, not 48.
2. 6 x 8 = 48
3. 6/2 = 3. therefore it fits the equal or greater sign
4. 8/2 = 4. it fits the greater or equal sign
5. if x is 6, 6 is less than 8. which makes the number sentence true
6. if x is 8, it is therefore not less than 8 but equal.
7. 5 x 6 is 30. Therefore 30 is not less than 30 but equal
8. 5 x 8 is 48. 48 is not less than or equal to 30
The answers provided are in reference to the questions below;
In each row of the table, select True or false if the number substituted for x results in a true or false number sentence
True False
6x = 48 when x = 6
6x = 48 when x = 8
x/2 ≥ 3 when x = 6
x/2 ≥ 3 when x = 8
x < 8 when x = 6
x < 8 when x = 8
5x < 30 when x = 6
5x < 30 when x = 8
Find more sentences regarding number sentences;
https://brainly.com/question/17322770
#SPJ1
Please help and explain PLEASE HELP PLEASE :( Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help
Answer:
C. 10
Step-by-step explanation:
You want to know the bin size in a histogram with bin boundaries 10.5, 20.5, 30.5, ....
Bin sizeThe size of the bin is the difference between its boundary values. Here, all of the bins are the same size:
20.5 -10.5 = 10
The bin size is 10.
__
Additional comment
The bin boundaries are typically chosen so that no data value can fall on the boundary, but must be unambiguously allocated to one bin or another. When the data values are integers, it is not uncommon to have the bin boundary be halfway between two integers.
Here, the boundary being 20.5 means a score of 20 will be counted in the bin to the left, and 21 will be counted in the bin to the right.
The boundary value shown at the right edge of the graph is not 100.5, as we might expect. However, we can reasonably assume that a test score of 100 would be counted in the bin with upper boundary 100, without any ambiguity.
Answer: 10
Step-by-step explanation:
The size of each value marker
In order to estimate the average electric usage per month, a sample of 121 houses was selected and the electric usage was determined. Assume a population standard deviation of 370 kilowatt-hours. The standard error is 33.64. Find the size of the margin of error at 95% confidence.
a. 1.64
b. 1.96
c. 55.33
d. 65.93
If the standard error is 33.64, the size of the margin of error at 95% confidence is 65.93. So, correct option is D.
The margin of error (ME) can be calculated using the formula:
ME = z* (standard error)
where z is the z-score from the standard normal distribution corresponding to the desired level of confidence. For 95% confidence, z is 1.96.
Substituting the values given in the problem, we have:
ME = 1.96 * 33.64 = 65.93
Therefore, correct option is D.
This means that if we take multiple random samples of size 121 from the population, and calculate the sample mean and confidence interval for each sample, we can expect the true population mean to fall within 65.93 units above or below the sample mean, 95% of the time.
To learn more about population click on,
https://brainly.com/question/15099929
#SPJ1
The Mackinac Bridge in Michigan is 1158 meters long. The Tsing Ma Bridge in Hong Kong is 97 meters longer than the Golden Gate Bridge in California. Together, all three bridges have a length of 3815 meters. How long is the Tsing Ma Bridge?
Lenght of Tsing Ma Bridge in Hong Kong is, 1,377 meters
Given that;
The Mackinac Bridge in Michigan is 1158 meters long.
And, The Tsing Ma Bridge in Hong Kong is 97 meters longer than the Golden Gate Bridge in California.
Let the length of Golden Gate Bridge = x
Then, Lenght of Tsing Ma Bridge in Hong Kong = x + 97
Since, Together, all three bridges have a length of 3815 meters.
Hence, We get;
1158 + x + (x + 97) = 3815
1255 + 2x = 3815
2x = 2,560
x = 1,280 meters
Thus, Lenght of Tsing Ma Bridge in Hong Kong = x + 97
= 1280 + 97
= 1,377 meters
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
the amount harry is paid each day, f(x), is a function of the number of hours, x, he works. the function f(x)=10x+25 models this situation. harry can work, at most, 4 hours each day. what is the best domain of the function in this context?
The total amount paid to harry in past week, is 299.28.
We know that,
Amount is the sum or the total value.
For example, if A purchase 2 kg rice at the price of 40 rs/kg, the amount will be 40×2= 80 rs.
Given that,
The amount paid to Harry for 1 hour = $8.60
Since, Harry worked for 33 hours,
So, The amount paid to Harry for 33 hours = 8.60×33=283.8
Harry gets half times more amount than hourly rate and also gets bonus for last 3 days
So for last 3 days the extra amount paid to Harry
= 3×1/2×8.60+3×1/10×8.60
= 12.9+2.58
=15.48
So the total amount paid to harry = 283.8+15.48=299.28
To know more about amount on :
brainly.com/question/28244711
#SPJ1
complete question:
Harry is paid £8.60 per hour for the first 30 hours he works each week. After 30 hours he is paid 1 and a half times the hourly rate.
Last week Harry worked 33 hours. He was also paid a bonus of 1/10 of his earnings
Calculate how much in total Harry was paid last week
Write each number in scientific notation
Answer:
There is nothing to write about my brother
Step-by-step explanation:
There is a scientific notation moment when shrek had to hit the griddy and said "i said right foot creep"