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jenyasd209 [6]
3 years ago
15

3. Evaluate the expression (-10) - (-4)

Mathematics
1 answer:
STatiana [176]3 years ago
7 0

Answer:

-6

Step-by-step explanation:

(-10) - (-4)

-10 +4 (because negative multiply by negative is positive)

= -6 (because -10+4 means different signs means you subtract and get the sign of the bigger number)

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A life guard in a tower 20 ft above sea level spots a struggling surfer at an angle of depression of 15 . How far is the surfer
GalinKa [24]

Answer: 19.31\ ft

Step-by-step explanation:

Given

The tower is at a height of h=20\ ft

the angle of depression is 15^{\circ}

Suppose the surfer is x ft away from the base of the tower

\therefore \text{From the figure, we can write}\\\\\Rightarrow \cos 15^{\circ}=\dfrac{x}{h}\\\\\Rightarrow x=h\cos 15^{\circ}\\\Rightarrow x=20\cos 15^{\circ}\\\Rightarrow x=19.31\ ft

Therefore, the surfer is at a distance of 19.31 ft from the base of the tower.

7 0
3 years ago
Please help me find the area of shaded region and step by step​
Bumek [7]

Answer:

Part 1) A=60\ ft^2

Part 2) A=80\ cm^2

Part 3) A=96\ m^2

Part 4) A=144\ cm^2

Part 5) A=9\ m^2

Part 6) A=(49\pi -33)\ in^2

Step-by-step explanation:

Part 1) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle

The area of rectangle is equal to

A=bh

where

b is the base of rectangle

h is the height of rectangle

so

A=(12)(7)-(8)(3)

A=84-24

A=60\ ft^2

Part 2) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior square

The area of square is equal to

A=b^2

where

b is the length side of the square

so

A=(12)(8)-(4^2)

A=96-16

A=80\ cm^2

Part 3) we know that

The area of the shaded region is equal to the area of four rectangles plus the area of one square

so

A=4(4)(5)+(4^2)

A=80+16

A=96\ m^2

Part 4) we know that

The shaded region is equal to the area of the complete square minus the area of the interior square

so

A=(15^2)-(9^2)

A=225-81

A=144\ cm^2

Part 5) we know that

The area of the shaded region is equal to the area of triangle minus the area of rectangle

The area of triangle is equal to

A=\frac{1}{2}(b)(h)

where

b is the base of triangle

h is the height of triangle

so

A=\frac{1}{2}(6)(7)-(6)(2)

A=21-12

A=9\ m^2

Part 6) we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

The area of the circle is equal to

A=\pi r^{2}

where

r is the radius of the circle

so

A=\pi (7^2)-(3)(11)

A=(49\pi -33)\ in^2

7 0
3 years ago
A group of 50 New York psychology students got a mean score of 530 on the psychology GRE with a standard deviation of 80. These
lesantik [10]

Answer: No, New York students are not truly more nerdy than the California students.

Step-by-step explanation:

Since we have given that

Number of students in a group = 50

Mean score of New York psychology = 530

Mean score of California psychology = 515

Standard deviation = 80

So, we will find t-distribution first.

t=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{530-515}{\dfrac{80}{\sqrt{50}}}\\\\t=1.32

Let α = 5% = 0.05

So, t_{\alpha,2}=2.920

Since t < t(critical value)

No, New York students are not truly more nerdy than the California students.

3 0
3 years ago
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and thr
Sindrei [870]

Answer:

The rental rate for the Fords is of $12 per day.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the cost of a Nissan.

y is the cost of a Ford.

z is the cost of a Chevrolet.

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.

This means that:

3x + 2y + 4z = 106

Two Nissans, four Fords, and three Chevrolets cost $107 per day

This means that:

2x + 4y + 3z = 107

Four Nissans, three Fords, and two Chevrolets cost $102 per day.

This means that:

4x + 3y + 2z = 102

From the first equation:

4z = 106 - 3x - 2y

2z = 53 - 1.5x - y

z = 26.5 - 0.75x - 0.5y

Replacing into the third equation:

4x + 3y + 53 - 1.5x - y = 102

2.5x + 2y = 49

From the second equation:

2x + 4y + 3z = 107

2x = 107 - 4y - 3z

x = 53.5 - 2y - 1.5z

x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)

x - 1.125x = 53.5 - 2y - 39.75 + 0.75y

-0.125x = 13.75 - 1.25y

0.125x = 1.25y - 13.75

x = \frac{1.25y - 13.75}{0.125}

x = 10y - 110

Find the rental rate for the Fords.

We have to find y, so:

2.5x + 2y = 49

2.5(10y - 110) + 2y = 49

25y - 275 + 2y = 49

27y = 324

y = \frac{324}{27}

y = 12

The rental rate for the Fords is of $12 per day.

3 0
3 years ago
3 x 2/5 Multiplying Fractions
Softa [21]

Answer:  6/5  or  1 1/5 <--- (SIMPLIFIED)

~hope this helped, have a gr8 day/night my friend!~

Step-by-step explanation:

3 0
3 years ago
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