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2 years ago

The Longstocking Toy Company is coming up with a new summer toy - Tinker the

Mathematics

1 answer:

SVEN [57.7K]2 years ago

7 0

Answer:

face: hemisphere
hat: cone

Step-by-step explanation:

The diagram shows a cone atop a hemisphere. We associate the cone with the hat (because it is on top), and the hemisphere with the face.

The shapes use are ...

face: hemisphere

hat: cone

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In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula StartFraction

tensa zangetsu [6.8K]

The given options are:

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

(B)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.

(C)the central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.

(D)the central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

Answer:

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

Step-by-step explanation:

The area of the shaded sector can be determined using the formula:

$\frac{m\angle ZYX}{360^\circ} \cdot \pi r^2$

$m\angle XYZ=$Central angle of XYZ\\\pi r^2$=Area of a Circle$

$360^\circ =$Total Angle$

Therefore, the formula is:

$\dfrac{m\angle ZYX}{360^\circ} \cdot \pi r^2\\\text{Area of XYZ}=\dfrac{\text{Cental Angle of XYZ}}{\text{Total Angle}} X \text{Area of the Circle}$

Therefore, the formula is best explained by Option A.

7 0

2 years ago

PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

sergiy2304 [10]

Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

Let $p_1$ = proportion of drivers that were in compliance initially

$p_2$ = proportion of drivers that were in compliance one year later

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, the test statistics = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

Now, P-value of the test statistics is given by;

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = 0.00043

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

7 0

2 years ago

An expression is given: 2 open parentheses square root of k minus 1 close parenthesis plus square root of 8. If on adding negati

neonofarm [45]

Answer:

Possible value of k is √2

Step-by-step explanation:

The information given are;

The expression, 2·(√k - 1) + √8 to which may be added -6·√2 to obtain a rational number, we therefore have;

2·(√k - 1) + √8 - 6·√2 = R

Therefore, simplifying gives;

2·√k - 2 + 2·√2 - 6·√2 = 2·√k - 2 - 4·√2 = R

2·√k - 2 - 4·√2 + 2= R + 2 = R

2·√k - 2+ 2 - 4·√2 = R

2·√k + 0 - 4·√2 = 2·√k - 4·√2 = 2·(√k - 2·√2) = R

(√k - 2·√2) = R/2 = R

Therefore, √2 is a factor of √k such that √k - 2·√2 = R

Which gives k = x·√2, where x = a rational number

When x = 1, k = √2.

Therefore, a possible value of k is √2

3 0

2 years ago

a box holds nine smaller boxes. each of the smaller boxes holds nine plastic containers. each plastic contai.er holds nine bags.

svp [43]

So, basically ..you just multiply
9*9*9*9
6561

4 0

2 years ago