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Vadim26 [7]
2 years ago
11

How do you solve this?

Mathematics
1 answer:
zaharov [31]2 years ago
8 0
Angle 2 and angle 4 are vertical angles which makes them congruent
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If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it acc
fenix001 [56]

Answer:

13 newtons

Step-by-step explanation:

6 0
2 years ago
The diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 mi
Assoli18 [71]

Answer:

Probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.

Step-by-step explanation:

We are given that the diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 millimeters.

<em>Firstly, Let X = diameters of ball bearings</em>

The z score probability distribution for is given by;

          Z = \frac{ X - \mu}{\sigma} ~ N(0,1)

where, \mu = mean diameter = 106 millimeters

            \sigma = standard deviation = 4 millimeter

Probability that the diameter of a selected bearing is greater than 111 millimeters is given by = P(X > 111 millimeters)

    P(X > 111) = P( \frac{ X - \mu}{\sigma} > \frac{111-106}{4} ) = P(Z > 1.25) = 1 - P(Z \leq 1.25)

                                                  = 1 - 0.89435 = 0.1056

Therefore, probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.

4 0
2 years ago
 Amy​'s car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas s
Kazeer [188]

Answer:

10 gallons

Step-by-step explanation:

Amy​'s car's maximum capacity to hold gas = 19 gallons

present amount of gas  = 9 gallons

As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.

let assume she fills x gallons

then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.

lets write it mathematically

x + 9 = 19

subtracting 9 from both side

x + 9 - 9 = 19 - 9

=> x = 10

Thus, 10 gallons of gas is needed to fill the gas tank.

6 0
3 years ago
Find the solution to the syster<br> y = 2x = 5<br> y = X - 2
lana66690 [7]

Answer:

Both of these equations are in slope-intercept form. The slope-intercept form of a linear equation is: y=mx+b

Where m is the y-intercept value.

y=-2x+5

y=-2x+20

The slope of the two equations are: m1=−2 and m2=−2

Step-by-step explanation:

Because the have the same slope it means the lines represented by these two equations are either parallel or are the same line.

The y-intercepts for the two lines are:b1 = 5 and b1=20

3 0
3 years ago
Are the marks one receives in a course related to the amount of time spent studying the subject? To analyze this mysterious poss
sertanlavr [38]

Answer:

a) 98.522

b) 0.881

c) The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time.

Step-by-step explanation:

a.

As the mentioned in the given instruction the co-variance is first computed in excel by using only add/Sum, subtract, multiply, divide functions.

Marks y Time spent x y-ybar x-xbar (y-ybar)(x-xbar)

77                    40 5.1         1.3 6.63

63                     42 -8.9            3.3 -29.37

79                     37 7.1            -1.7 -12.07

86                     47 14.1            8.3 117.03

51                    25 -20.9  -13.7 286.33

78                     44 6.1            5.3 32.33

83                      41 11.1            2.3 25.53

90                     48 18.1            9.3 168.33

65                     35 -6.9           -3.7 25.53

47                    28 -24.9 -10.7 266.43

Covariance=\frac{sum[(y-ybar)(x-xbar)]}{n-1}

Co-variance=886.7/(10-1)

Co-variance=886.7/9

Co-variance=98.5222

The co-variance computed using excel function COVARIANCE.S(B1:B11,A1:A11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted co-variance is 98.52222.

b)

The correlation coefficient is computed as

Correlation coefficient=r=\frac{sum[(y-ybar)(x-xbar)]}{\sqrt{sum[(x-xbar)]^2sum[(y-ybar)]^2} }

(y-ybar)^2 (x-xbar)^2

26.01        1.69

79.21       10.89

50.41             2.89

198.81       68.89

436.81       187.69

37.21       28.09

123.21        5.29

327.61        86.49

47.61         13.69

620.01         114.49

sum(y-ybar)^2=1946.9

sum(x-xbar)^2=520.1

Correlation coefficient=r=\frac{886.7}{\sqrt{520.1(1946.9)} }

Correlation coefficient=r=\frac{886.7}{\sqrt{1012582.69} }

Correlation coefficient=r=\frac{886.7}{1006.2717 }

Correlation coefficient=r=0.881

The correlation coefficient computed using excel function CORREL(A1:A11,B1:B11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted correlation coefficient is 0.881.

c)

The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time. It means that as the study time increases the marks of student also increases and if the study time decreases the marks of student also decreases.

The excel file is attached on which all the related work is done.

Download xlsx
7 0
3 years ago
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