Estimate the:
length of a pen
length of a swimming pool
length of a marathon race​

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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The True- False of given statements of Solutions of Equations are justified.

1.13 False. The solution set to a system of three equations in three unknowns can be a point, a line, or a plane. It depends on the system of equations and how they intersect in three-dimensional space.

1.14 False. A system of linear equations can have infinitely many solutions, one solution, or no solutions. It depends on the coefficients of the equations and the rank of the coefficient matrix.

1.15 False. The solution set to a consistent rank 2 linear system in four unknowns would be a plane in four-dimensional space, not a line.

1.16 False. A system of four equations in four unknowns may not have a solution, or it may have infinitely many solutions or one solution. It depends on the coefficients of the equations and the rank of the coefficient matrix.

1.17 False. A system of four equations in four unknowns can have infinitely many solutions or one solution, but it cannot have at most one solution.

1.18 True. The rank of a system is always less than or equal to the number of equations in the system.

1.19 (a) False. If (i) has exactly one solution, it does not necessarily mean that (ii) will have exactly one solution. It depends on the coefficients of the equations in (ii).

(b) False. If the solution set of (i) is a line, it does not necessarily mean that the same is true for (ii). It depends on the coefficients of the equations in (ii).

(c) True. If (i) has no solutions, then the same is true for (ii), since (ii) is equivalent to (i).

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There is an estimate that 340 of the school's 425 students have at least one sibling.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

To estimate the number of students in the school who have at least one sibling, we can use the proportion from the sample.

The proportion of students with at least one sibling can be calculated as:

= 96/120

= 0.8

Expected number of students with at least one sibling in the school:

= Proportion x Total number of students

= 0.8 x 425

= 340

Therefore, it would expect 340 of the 425 students at the school to have at least one sibling.

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Answer: $18.75

Step-by-step explanation:

1 - 3/8 = 5/8

12 x 5/8 = 7.5

7.5 x 2.5 = 18.75

Dave spent $18.75, in filling his car's tank of capacity 12 gallons up to the capacity, which was 3/8th filled already, at the unit rate of $2.50 per gallon of gas.

The unit rate is the quantity (cost/distance/time, etc.) for one unit of another quantity (cost/distance/time, etc.).

In the question, we are informed that the gas tank of Dave's car has a capacity of 12 gallons. The tank was 3/8 full before Dave filled it to capacity. It cost him $2.50 per gallon of gas.

We are asked the amount Dave spent.

The unit rate of gas is $2.50 per gallon.

To find the total amount spent by Dave, we need to find the volume of gas he filled and then multiply that volume with the unit rate.

The capacity of Dave's car's tank = 12 gallons.

Gas it already had = 3/8th of capacity,

or, gas it already had = 3/8 * 12 = 4.5 gallons.

Therefore, the volume of gas Dave filled = 12 - 4.5 gallons = 7.5 gallons.

The amount spent by Dave = Volume filled*Unit rate = $ 7.5 * 2.5 = $18.75.

Therefore, Dave spent $18.75, in filling his car's tank of capacity 12 gallons up to the capacity, which was 3/8th filled already, at the unit rate of $2.50 per gallon of gas.

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Answer:

10x10x10 or 10*3......

A probability value equal to or smaller than 0.05 would indicate that Gaurav's null hypothesis should be rejected at the 5% significance level.

In hypothesis testing, the significance level, denoted as alpha (α), is the predetermined threshold used to determine whether to reject the null hypothesis.

Gaurav has specified a 5% significance level, which means he wants to control the probability of making a Type I error (rejecting the null hypothesis when it is true) at 5% or less.

If Gaurav were to conduct a test and calculate the p-value, he would compare it to the significance level of 0.05.

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

If the p-value is less than or equal to the significance level (p ≤ α), it indicates that the observed difference is unlikely to occur by chance alone under the assumption of the null hypothesis.

Gaurav would reject the null hypothesis and conclude that there is a significant difference between the average amount of medication his patients are taking and the national average.

Conversely, if the p-value is greater than the significance level (p > α), it suggests that the observed difference could reasonably occur by chance, and Gaurav would fail to reject the null hypothesis.

This would imply that there is no significant difference between the average medication amounts of Gaurav's patients and the national average.

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Bar graphs are used to represent the frequencies of a dataset using bars.

From the frequency table (see attachment), the dataset and their frequencies are represented as:

The dataset on Mica's histogram and their frequencies are:

Notice that the frequencies of Spaghetti and Hamburger on the frequency table differs from the frequencies plotted on Mica's histogram.

This means that, the bar graph is incorrect

Although the bar graph plotted by MIca is incorrect, the best type of display is the bar graph

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Answer:

2:3

Step-by-step explanation:

minutes per day on weekdays:minutes per day on weekends

90:135

It can be written in simpler form, because both numbers can be divided by 45

90÷2=45 and 135÷45=3

The ratio is 2:3.

Answer:

225

Step-by-step explanation:

x² -y³

Evaluate for x=3,y=−6

3²−(−6)³

3²−(−6)³

=225

The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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Answer:

392 ft²

Step-by-step explanation:

The composite figure can be divided into a rectangle, 2 triangles and a square

Area of rectangle = Length * width

Area of rectangle = 21 feets * 14 feets = 294 feet²

Area of triangle = 0.5 * base * height

Area of triangle = 0.5 * 7 * 7 = 24.5

AREA of square = a² = 7² = 49 feets²

Total area :

294 feets + (2 * 24.5) feets² + 49 feets²

294 + 49 + 49 = 392 ft²

What is the distance between (-5,2) and (4,-9). Use the distance formula, d= sqrt (x^2-x^1)^2 + (y^2-y^1)^2

substitute in the formula

Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

The value of Y when X = 4 in the regression line that has the slope of 2,5 is a) 26

The equation of a straight line with slope m and y-intercept b is given by  :

y = mx + b.

Where

1. y is the dependent variable (i.e., the value of y depends on x)

2. x is the independent variable

3. m is the slope of the line, representing the rate of change of y with respect to x

4. b is the y-intercept, the point where the line intersects the y-axis when x = 0.

This equation can be used to describe the relationship between two variables, and it can be used to make predictions about the value of y for a given value of x, or to find the value of x for a given value of y.

From the question we have the following information :

1. Slope ( or m ) is 2.5

2. The intercept ( y-intercept or b ) is 16

So, using the values given (slope = 2.5, y-intercept = 16), we have:

y = mx + b

y = 2.5x + 16

When X is 4, substituting X with 4 in the equation gives us:

y = 2.5 * 4 + 16 = 26

So the value of Y when X is 4 is 26. Answer: a) 26.

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Answer:

x=42

Step-by-step explanation:

step 1: multiply 3 to both sides of the equation to isolate x

then you get x=14x3=42

x=42

Answer:

X=42

Step-by-step explanation:

14 * 3= 42

14 = x/3

14= 42/3

divide

14=14

Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

Answer:

6 units²

Step-by-step explanation:

The formula for the area of triangle is 0.5bh where b is the length of the base and h is the (perpendicular) height.

A=0.5bh

A=0.5(4)(3)

A=6

Answer:

y=3x+2

Step-by-step explanation:

First find the slope or m in the line of equation y=mx+b

to find slope you need two points, plug in to y2-y1 / x2-x1

so lets use points (0,2) (1,5)

5-2 / 1-0 = 3

m=3

we have y=3x + b

now we find b by pugging in a point, let's use (0,2)

2 = 3(0) + b

b= 2

y=3x+2

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The polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.

In this problem we have three shapes related to circle-like and ellipse-like arcs (circle, semicircle, ellipse) and a regular polygon.

Circles are closed figures created by a arc whose radius of curvature is the same at every point and ellipses are closed figures created  by a arc whose radius of curvature varies in the following interval: a ≤ r ≤ b, where a, b are the lengths of the semiaxes.

Polygons are closed figures created by a finite number of line segments and therefore the concept of radius of curvature is not applicable.

Therefore, the polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.

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Answer:

8 units

Step-by-step explanation: Hope it helps.

Answer:

a. 3 cm

b. 6 km

Step-by-step explanation:

to be completely honest, I just shoot my answer based on the pattern.

if you notice that when the scale is 4 cm, the actual distance is 5 km. When the distance is 4 km, the scale should probably be 3 cm. It's the same with the 5 cm scale, then the distance should be 6 km

Step-by-step explanation:

Use ratios to solve it

a)

x = 4*4/5 = 3.2 cm

b)

x = 5*5/4 = 6.25 km

Answer:

so your awnser would be

Step-by-step explanation:

Daddy

Answer:

RS = 38

ST = 22

RT = 60

Step-by-step explanation:

Answer:

no it's different 30% would be 12 and 40% would be 16 if it was going into 30 now mark as brainliest

Answer:

In both cases you are really multiplying the same numbers together.

Step-by-step explanation:

30% of 40 would be 30 x 40 x 0.01 = 12

or 0.30 x 40 = 12

40% of 30 would be 40 x 30 x 0.01 = 12

or 30 x 0.40 = 12

Answer:

D. Average deviation from the mean in the group must be squared to be meaningful.

Step-by-step explanation:

The average variability from mean is not calculated with mean square of the selected group. The deviation scores calculated by subtracting participant score from the mean.  

Answer:

S = v1 t1 = 7 t1    traveling downstream

S = v2 t2 = 5 t2    traveling upstream

7 t1 = 5 t2

7 (6 - t2) = 5 t2     since t1 + t2 = 6

42 - 7 t2 = 5 t2

t2 = 42 / 12 = 3.5 hrs so t1 = 2.5 hrs

S = 7 t1 = 7 * 2.5 = 17.5 mi

Also, S = 5 t2 = 5 * 3.5 = 17.5 mi

Answer:

I think there is 140 questions