The number of hours that the grade 7 student spends studying can be found to be 2 hours.
How to find the number of hours ?We are told that the grade 7 student gets 4 hours of free time after school and from that time, they spend 1 / 2 of it studying.
This means that the number of hours spent by the grade 7 student in studying can be found by the formula:
= Free time x proportion of time spent studying
= 4 hours x 1 / 2
= 4 / 2
= 2 hours
In conclusion, the grade seven student spent 2 hours studying.
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The full question is:
A typical grade 7 student is reported to have about 4 hours of free time after school on weekdays. They spend 1 / 2 of this time studying.
How many hours does the grade 7 students spend in studying?
Aubrey launches a toy rocket from a platform. The height of the rocket in feet is given by ℎ = − 16 � 2 + 64 � + 36 h=−16t 2 +64t+36 where � t represents the time in seconds after launch. What is the appropriate domain for this situation?
The domain of the height function is:
t ∈ [0, 4.5]
What is the appropiate domain of the function?We know that the height of the function is modeled by the quadratic equation:
h = -16t² + 64t + 36
The domain is the set of the possible values of t.
The initial value of the domain is at t = 0s, to find the maximum value, we need to find the value of t such that the height is zero (when the rocket hits the ground)
Then we need to solve:
-16t² + 64t + 36 = 0
Using the quadratic formula we will get:
[tex]t = \frac{-64 \pm \sqrt{64^2 - 4*(-16)*36} }{2*-16} \\\\t = \frac{-64 \pm80}{-32}[/tex]
We only care for the positive solution, which is:
t = (-64 - 80)/-32 = 4.5
Then the domain is [0, 4.5]
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x-3=3-x the equation has one solution A value of x that makes the equation true is ____ which when substituted into the equation and simplified makes the equation turn into _____
Step-by-step explanation:
x - 3 = 3 - x
x = -x + 3 + 3
2x = 6
x = 3
blank1: 3
blank2: 3
7 - 2x = 13
solve for X
Answer: x = -3
negative Three
Number of Years Since Investment Made, x Value of Investment ($), f(x) 1 Submit Answer 11,858.03 2 V 10,109.59 8,576.00 A linear function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier/base of this function is approximately 4 7,318.76 Privacy Policy Terms of Service Copyright © 2023 Dalt attempt 1 out of 2
The least-squares regression line's equation is thus: f(x) = -1,246.78x + 10,381.72
How to calculate the regressionThe line for which the sum of the squares of the residuals is as tiny as it can be is known as the least square regression line, or LSRL for short. M=rsysx, where r is the dataset's correlation coefficient, provides the LSRL's slope.
n = 4
∑x = 10
∑y = 38,862.38
∑xy = 337,655.08
∑x² = 30
b = (4337,655.08 - 1038,862.38) / (4 × 30 - 10²) = -1,246.78
a = (38,862.38 - (-1,246.78) × 10) / 4 = 10,381.72
Based on this, least-squares regression line's equation is thus: f(x) = -1,246.78x + 10,381.72
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Factor f(x) = x2 + 10x + 16
Answer:
To factor f(x) = x^2 + 10x + 16, we need to find two numbers whose sum is 10 and whose product is 16.
The two numbers are 2 and 8, since 2 + 8 = 10 and 2 × 8 = 16.
Therefore, we can write:
f(x) = x^2 + 10x + 16
= x^2 + 2x + 8x + 16
= (x^2 + 2x) + (8x + 16)
= x(x + 2) + 8(x + 2)
= (x + 2)(x + 8)
So the factorization of f(x) is (x + 2)(x + 8).
how do you find surface area and volume of a triangular prism
The surface area of a triangular prism can be found by the formula SA = 2(Ab) + Ph. The volume can be found by V = Ab × h.
We have,
to find the volume and surface area of a triangular prism:
To calculate the surface area of a triangular prism, one must sum the areas of all its faces. This can be done by computing the area for each component of the prism and then combining them; utilizing the formulas:
SA = 2(Ab) + Ph
Where SA stands for Surface Area, Ab is the Area of the base (triangle), P representing the Perimeter of the base (triangle) and h denoting the Height of the triangular prism.
Moreover, to ascertain the volume of a triangular prism, the equation is:
V = Ab × h
in which V stands for Volume, Ab is still the Area of the triangular base and h is representing the Height of the triangle that comprises the prism.
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a catering company uses a linear function to determine the total cost of parties. the following table shows the costs for dinner parties with varied numbers of guests. what is the cost to cater a dinner party with 90 guests?gueststotal cost30$31560$555$720$795$870$945
For a catering company, which used the linear function for calculating the total cost of parties, the cost to cater a dinner party with 90 guests is equals to the $42750.
We have a table form data of total cost of parties for a catering company. There is use of linear function to determine total cost of parties. Table look like as below,
Cost for dinner parties | number of guests
(each guest)
$315 30
$555 60
We have to determine the cost to cater a dinner party with 90 guests. For this we use simple multiplication arithmetic method. As we see in table, cost of cater a dinner party with 30 guests = $315 for each , that is cost for one guest = $315
so, cost of cater a dinner party with 30 guests = 30 × $315 = $ 9450
Similarly, when number of guests is 60 in count, cost of cater a dinner party = $555 for each one
So, total cost of cater a dinner party with 60 guests = 60× $555 = $ 33300
Now, we have total guest = 90
The cost to cater a dinner party with 90 guests
= cost to cater a dinner party with 30 guests + cost to cater a dinner party with 60 guests = $9450+ $33300
= $42750
Hence, required value is $42750.
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scott takes gets a student loan to go to college after high school.If he pays 750 interest at a rate of 3%,how much must the loan have been for originally.
Answer:
$25,000
Step-by-step explanation:
To calculate the original amount of the student loan that Scott took, we can use the formula for calculating simple interest:
Simple Interest = Principal (loan amount) x Rate x Time
Given:
Interest (I) = $750
Rate (R) = 3% or 0.03 (as a decimal)
Let's assume the time (T) for the loan is one year, as the rate is given as an annual rate.
Plugging in the values into the formula:
750 = Principal x 0.03 x 1
750 = 0.03 Principal
To solve for Principal, we can divide both sides of the equation by 0.03:
Principal = 750 / 0.03
Principal = $25,000
So, the original amount of the student loan that Scott took was $25,000.
a sample of single persons receiving social security payments revealed these monthly benefits: $825, $713, $1,041, $1,028, $919, and $1,008. how many observations are below the median?
Therefore, there are 2 observations below the median that is $713 and $825.
To find the median of a data set, we first need to arrange the values in order from smallest to largest. Once the values are in order, we can determine the middle value of the data set. If the data set has an odd number of values, then the median is the middle value. If the data set has an even number of values, then the median is the average of the two middle values. Once we have found the median, we can count the number of observations that are below the median by comparing each observation to the median. If the observation is less than the median, then it is considered to be below the median. First, we need to find the median of the data set. To do so, we can arrange the values in order from smallest to largest:
$713, $825, $919, $1,008, $1,028, $1,041
The median is the middle value, which is $973.
Next, we count the number of observations that are below the median, which are:
$713 and $825
Therefore, there are 2 observations below the median.
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Help me out with this please
We can actually see that moment of force can be defined as the effectiveness of a force to make an object rotate in its axis. It is measured in Newton meters (N-m).
A uniform beam is known as a structural element which has a uniform cross-section and material properties along its length.
What is force?Force can be defined as the influence which makes a body or an object to undergo change in position, motion or deformation. It is a vector quantity which reveals the interaction that exists between two objects.
Moment of force is seen to determine how much force is required to produce rotational motion in an object around a pivot point.
Moment of force = Force x Perpendicular distance from axis of rotation.
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Samantha's car used 2 5/8 gallons to travel 147 miles. How many miles can the car go on one gallon of gas?
let's firstly convert the mixed fraction to improper fraction.
[tex]\stackrel{mixed}{2\frac{5}{8}}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} gallons&miles\\ \cline{1-2} \frac{21}{8} & 147\\[1em] 1& m \end{array} \implies \cfrac{\frac{21}{8}}{1}~~=~~\cfrac{147}{m}\implies \cfrac{21}{8}=\cfrac{147}{m} \\\\\\ 21m=(8)(147)\implies m=\cfrac{(8)(147)}{21}\implies m=56[/tex]
In Exercises 3-8, use the diagram of OD with LEDF & LFDG to find the indicated measure.
(Please help me with this assignment, i have been going over this since 2 hours. This is geometry.)
The required sides are solved to get
2. angle EFG = 160 degrees
4. angle EHG = 200 degrees
5. arc length of EHG = 200 degrees
6. arc length of FEG = 280 degrees
How to find angle EFGIn the problem it is given that angle EDF = angle FDG = 80 degrees.
Knowing that intercepted arc and the central angle are equal we have that
2. angle EFG = 80 degrees + 80 degrees = 160 degrees
4. angle EHG = 360 - angle EFG
= 360 - 160
= 200 degrees
5. arc length of EHG = angle EHG = 200 degrees
6. arc length of FEG
= 360 - 80
= 280 degrees
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A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?
A. The population mean is more than 110.
B. The population mean is less than 150.
C. The population mean is between 140 and 150.
D. The population mean is more than 140.
E. The population mean is less than than 125.
The correct option is E. The population mean is less than 125. As, 125 is does not comes in the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.
The 90% confidence interval for the mean of the population is computed to be 135 to 160. This means that we are 90% confident that the true population mean falls within this range.
Since 125 is not within the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.
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errors that pertain to anything in the research process except sample size are known as: a. intentional field work error. b. non-sampling error. c. field error. d. sampling error.]
Errors that pertain to anything in the research process except sample size are known as option b. non-sampling error.
Non-sampling errors are errors that occur in the research process other than those related to sample size. These errors can arise at any stage of the research process, including data collection, data processing, analysis, and interpretation. Examples of non-sampling errors include errors in data entry or coding, selection bias, measurement bias, interviewer bias, and response bias. Non-sampling errors can have a significant impact on the accuracy and validity of research findings and should be carefully controlled and minimized to the extent possible.
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a jar is filled with red, white, and blue tokens that are equivalent except for their color. the chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. if the number of tokens of every color is a multiple of 3, what is the smallest possible total number of tokens in the jar?
The smallest possible total number of tokens in the jar is 27, with 6 red tokens, 3 white tokens, and 18 blue tokens.
Let's assume that the jar has "r" red tokens, "w" white tokens, and "b" blue tokens. Since the probability of selecting a red token and then a white token is the same as selecting a blue token, we can write the following equation
(r/3) × (w/3) = (b/3) × ((r + w)/3)
Simplifying this equation, we get
rw = b(r + w)
Now, we need to find the smallest possible total number of tokens in the jar. Since r, w, and b are all multiples of 3, we can write
r = 3x
w = 3y
b = 3z
Substituting these values in the equation rw = b(r + w), we get
9xy = 9z(x + y)
Simplifying this equation, we get
xy = z(x + y)
Since x, y, and z are all integers, we can say that z divides xy. Therefore, we can write
z = kd
xy = k(d x + d y)
where k and d are integers.
Now, we need to find the smallest possible value of (r + w + b) = 9(x + y + z) that satisfies the above conditions. Since z is a multiple of 3, we can start with k = 3. Also, we want to minimize (x + y + z), so we can start with d = 2. Substituting these values, we get
z = 3 × 2 = 6
xy = 3(2x + 2y) = 6(x + y)
The smallest possible values of x and y that satisfy this equation are x = 2 and y = 1. Substituting these values, we get
r = 3x = 6
w = 3y = 3
b = 3z = 18
Therefore, the smallest possible total number of tokens in the jar is
r + w + b = 6 + 3 + 18 = 27
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Please help me with this homework
Answer: 50°
Step-by-step explanation: Sum of all Angles in a triangle is 180°
jose has a storage container in the shape of a right rectangular prism. the volume of the container is 39.442 cubic meters, the length is 4.1 meters, and the width is 3.7 meters. what is the height of jose's storage container?
The height of the prism shaped storage container that Jose is using is found to be 2.585 meters,
We can use the formula for the volume of a rectangular prism to find the height of Jose's storage container.
Volume of a rectangular prism = length x width x height
It is given that the volume is 39.442 cubic meters and the length and width is 4.1 meters and 3.7 meters. Putting the values and solve for the height:
39.442 = 4.1 x 3.7 x height
Simplifying this equation, we get:
39.442 = 15.27 x height
Dividing both sides by 15.27, we get:
height = 2.585 meters
Therefore, the height of storage container is 2.585 meters.
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Ali paints with watercolors on a sheet of paper 20 in. wide by 15 in. high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 in. How wide is the strip of the mat showing around the picture?
When the mat's perimeter is 102 inches, the strip that shows around the picture is 8 inches broad.
What is perimeter?The perimeter of a shape is the distance around its edge. The perimeter of a form is the length of its contour. To calculate the perimeter of a rectangle or square, sum the lengths of all four sides. The perimeter of a shape is the distance around its exterior. Perimeter is calculated by summing the lengths of all the sides of a form.
Here,
length of paper, l = 20 inch
width of paper, w = 15 inch
perimeter = 102 inch
Let x be the strip of mat,
[tex]\text{l = 20 + 2x}[/tex]
[tex]\text{w = 15 + 2x}[/tex]
[tex]\text{perimeter = 2(l + w)}[/tex]
[tex]102=2\times(20+2x+15+2x)[/tex]
[tex]51=35+2\text{x}[/tex]
[tex]2x=16[/tex]
[tex]\boxed{\bold{x=8 \ inches}}[/tex]
The strip of the mat showing around the picture is 8 inches wide when the perimeter of the mat is 102 inch.
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Convert 13 weeks to seconds
Answer:
7862400Seconds
Step-by-step explanation:
13Weeks=
7862400Seconds
Answer:7.862e+6
Step-by-step explanation:
gogled it
In which quadrant does (-4,2) lie ?
Answer:
In the point (4,-2) abscissa is positive and ordinate is negative. So, it lies in fourth quadrant.
Consider this data set:
{49, 50, 45, 23, 35, 66, 34, 74, 54, 50}
The mean is:
The median is:
The mode is:
The range is:
Suppose the value 60 is added to the data set.
The mean increased by:
The median increased by:
The mode is:
The range is:
Step-by-step explanation:
The mean is: 48
The median is: 49.5
The Mode is: 74
The Range is: 51
The mean is increased by: 1.09
The median is increased by: 0.5
The mode is: 74
The Range is: 51
What is the equation of the line that is parallel to the linear graph of y=2x-1 and passes through the point (-1,1)?
Answer:
y=2x+3 or option C is the correct answer.
Answer: C. y=2x+3
Step-by-step explanation:
Given:
y=2x-1 and new line passes through (-1,1)
Rules:
>A line is parallel to another line if the slopes are the same.
>Also, y=mx+b m=slope b=y-intercept
Solution:
y=2x-1 In the line given equation slope m=2 so slope for the new line will be the same
m=2 (-1,1) = [tex](x_{1} ,y_{1})[/tex] because you now have the slope and a point. Use point
slope form to write an equation
[tex]y-y_{1} =m(x-x_{1} )[/tex]
y-1=2(x-(-1)) > simplify
y-1=2(x+1) > distribute
y-1=2x+2 > add 1 to both sides
y=2x+3
PLEASE HELP!!!
Using the two-way table, what percentage of the students that do not like to travel out of state like camping? Round to the nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
A 32%
B 34%
C 38%
D 42%
The percentage of the students that do not like to travel out of state like camping is 34%. The Option B is correct.
What percentage of non-travelers like camping?Given that:
The number of students who do not like to travel out of state and like camping = 38
The total number of students who do not like to travel out of state is 112.
The percentage of non-travelers who like camping will be calculated as:
= (Number of non-travelers who like camping / Total number of non-travelers) x 100%
= (38 / 112) x 100%
= 0.33928571428 * 100%
= 33.93%.
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A line goes through the points (8,1) and (2,−9). Find its slope. Enter your answer as a simplified improper fraction, if necessary. Do not include "m=" in your answer.
Answer:
-5/3
Step-by-step explanation:
The slope of a line passing through two points (x1,y1) and (x2,y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points (8,1) and (2,-9), we can substitute the values into the formula:
slope = (-9 - 1) / (2 - 8)
slope = -10 / -6
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
slope = (-10 / 2) / (-6 / 2)
slope = -5 / 3
Therefore, the slope of the line passing through the points (8,1) and (2,-9) is -5/3.
Find the volume of this composite object!
(use 3 for pi)
The volume of the composite figure is 123 cm³
How to determine the volumeFrom the image shown, we can see that the composite is made up of a cone and a rectangular prism.
The volume of a rectangular prism is expressed as;
V = lwh
Such that the parameters are;
l, w and h are the length, width and height of the prismV is the volume.Substitute the values
Volume, V = 5 × 1 × 12
Multiply the values
Volume = 60 cm³
The formula for the volume of a cone is expressed as;
Volume = πr²h/3
Substitute the values
Volume = 3 × 3² × 7/3
Multiply the values
Volume = 63 cm³
Then, the total volume = 63 + 60 = 123 cm³
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Jim runs each lap in 6 minutes. He will run at least 7 laps today. What are the possible numbers of minutes he will run today? Use t for the number of minutes he will run today. Write your answer as an inequality solved for t.
The possible numbers of minutes Jim will run today is represented by the inequality: 42 ≤ t ≤ 6x
How to determine the possible numbers of minutes Jim will run todayIf Jim runs at least 7 laps today, then the minimum number of minutes he will run is 7 laps x 6 minutes/lap = 42 minutes.
To find the maximum number of minutes he will run, we need to consider the possibility that he runs more than 7 laps.
Let's say he runs x laps in total, where x is greater than or equal to 7. Then the total number of minutes he will run is n laps x 6 minutes/lap = 6n minutes.
Therefore, the possible numbers of minutes Jim will run today can be represented by the inequality: 42 ≤ t ≤ 6x
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a father is 30 years older than his son. he will be three times as old as his son after 5 years. what is the father's present age?
Since, the father is 30 years older than his son. Then, the son's age is 10 years old. Therefore, the father's age is x+30 = 40 years old.
Let's denote the son's current age as S and the father's current age as F. From the information given, we know:
1. F = S + 30 (the father is 30 years older than his son)
2. F + 5 = 3 * (S + 5) (the father will be three times as old as his son in 5 years)
Now, we need to solve for F:
Step 1: Substitute the first equation with the second equation:
(S + 30) + 5 = 3 * (S + 5)
Step 2: Simplify the equation:
S + 35 = 3S + 15
Step 3: Move all terms with S to one side and constants to the other side:
35 - 15 = 3S - S
20 = 2S
Step 4: Divide by 2 to isolate S:
S = 10
Now that we know the son's age, we can find the father's age using the first equation:
F = S + 30
F = 10 + 30
F = 40
The father's present age is 40 years old.
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What value is equivalent to 5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7?
A -71
B -75
C -99
D -11
E -83
The value that is equivalent to 5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 is 7
Evaluating the expressions equivalenceFrom the question, we have the following parameters that can be used in our computation:
5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7
Evaluate the expressions in bracket
So, we have
5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 = 20 − 20 + 7
Evaluate the sum and the difference
So, we have
5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 = 7
Hence, the soluton is 7
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a pollster wishes to estimate the proportion of united states voters who favor capital punishment.how large a sample is needed in order to be 98% confident that the sample proportion will notdiffer from the true proportion by more than 3%?
The sample proportion will not differ from the true proportion by more than 3% for 98% confident is equal to 1508 voters.
Use the following formula to determine the sample size needed to estimate a proportion with a given margin of error and confidence level,
n = (Z² × p × (1-p)) / E²
where,
n = sample size
Z = Z-score associated with the desired confidence level
= 98% confidence level corresponds to a Z-score of 2.33
p = the proportion we are trying to estimate
Use 0.5 as a conservative estimate the largest possible sample size.
E = the desired margin of error
= 0.03
Plugging in the values we have,
n = (2.33² × 0.5 × (1-0.5)) / 0.03²
n = 1508.02
= 1508 voters (Rounding up )
Therefore, a sample size of at least 1508 voters to be 98% confident sample proportion will not differ from true proportion by more than 3%.
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I need help on this please hurry.
Answer:
The correct answer would be D
Given that Neil retrieved 3470 grams of soil, and the average soil density on mars is 3.93 g/cm^3, we can make the equation of 3470/3.93 to get 882.951654, or ~882.95
