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3 years ago

7. A scatter plot was created to show the relationship

Mathematics

1 answer:

Ksju [112]3 years ago

7 0

Answer:

1020 students

Step-by-step explanation:

Given the trend line equation :

y = 0.1x + 18,

where y is the total number of staff members and x is the total number of students.

Using the equation, the predicted number of students in a school with 120 staffs ;

y = 120

y = 0.1x + 18

120 = 0.1x + 18

120 - 18 = 0.1x

102 = 0.1x

x = 102 / 0.1

= 1020 students

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Iman has 6 packs of cards . Mateo has 10 packs of cards. between the two of them, they have 128 sports cards . how many sports c

kumpel [21]

iman has 48 cards and mateo has 80 cards

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3 years ago

A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

explain what does the constant rate of change means in the context, (basically what is the meaning of a constant rate change.).

LUCKY_DIMON [66]

Here the topic is "functions." Roughly speaking, we have a box. Input enters at one end and output exists at the other. Now, if every input value x (such as 2) is doubled by the box, every output value is 2x: (0,0), (1,2), (2,4), etc.

We call this "doubling" a "constant rate of change.

If you plot the points given, you'll see that they all are on a straight line. That straight line has the slope 2: y = 2x. Again, 2 is the "constant rate of change" here.

If you drive at a steady 55 mph, you are covering 55 miles during every hour behind the wheel. Again, 55 is a "constant rate of change."

4 0

3 years ago

Read 2 more answers

the area of a window is 192 in squared. The width if the window is four inches more than half the length of the window. What are

Leya [2.2K]

Answer:

Length = 16 inches and width = 12inches

Step-by-step explanation:

A = 192 in² . The width is 4 + 1/2x. therefore let x = length

Area = LW

192 = x(4 + 1/2 x)

192 = 4x + 1/2x²

384 = 8x + x² Multiply each term by 2 to make a

384 + 16 = x² + 8x + 16 Complete the square

400 = (x + 4)²

$\sqrt{400} = \sqrt{(x + 4)^2}$

± 20 = x + 4

20 = x + 4 or -20 = x + 4

20 - 4 = x or -20 - 4 = x

16 = x or -24 = x reject the negative amount

Length = 16

width = 4 + 1/2(16); 4 + 8 = 12

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3 years ago

For parallelogram ABCD, find m<1

monitta

Answer:

Step-by-step explanation:

the answer is

the angel m<1= 36°

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3 years ago