How many hours does the grade 7 students spend time in studying?(summarizing question)

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]

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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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

In 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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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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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.

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.

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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The domain of the height function is:

t ∈ [0, 4.5]

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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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

Answer: x = -3

negative Three

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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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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The possible numbers of minutes Jim will run today is  represented by the inequality: 42 ≤ t ≤ 6x

If 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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Answer:

In the point (4,-2) abscissa is positive and ordinate is negative. So, it lies in fourth quadrant.

The volume of the composite figure is 123 cm³

From 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;

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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The value that is equivalent to 5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 is 7

From 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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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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The percentage of the students that do not like to travel out of state like camping is 34%. The Option B is correct.

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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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.

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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Answer: 50°

Step-by-step explanation: Sum of all Angles in a triangle is 180°

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

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).

The least-squares regression line's equation is thus: f(x) = -1,246.78x + 10,381.72

The 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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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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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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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

When the mat's perimeter is 102 inches, the strip that shows around the picture is 8 inches broad.

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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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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Step-by-step explanation:

x - 3 = 3 - x

x = -x + 3 + 3

2x = 6

x = 3

blank1: 3
blank2: 3

Answer:

7862400Seconds

Step-by-step explanation:

13Weeks=

7862400Seconds

Answer:7.862e+6

Step-by-step explanation:

gogled it