The diagonals of a rhombus are of length 24cm and32cm.

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Deffense [45]

Answer:

a

f'(t) is negative

b

The unit is degC/min

c

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

Step-by-step explanation:

From the question we are told we are told that

The equation for the temperature of a cup of coffee place on a counter is

$H= f(t)$

Here t is the time in minutes the coffee was put on the counter

Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time

Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative

Generally the unit of the temperature is in degrees Celsius while that of time is in minutes

So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)

From the question we are told that

$|f(35)'| = 1.5$

i.e the rate of change of temperature after 35 minutes is 1.5

and

$|f(35)| = 68$

i.e the temperature of the cup of coffee after 35 minutes is 67 degC

Now after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate of change of the temperature of the cup of coffee is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

So

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

5 0

3 years ago

G two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. how m

vovikov84 [41]

Note :- If sample size n > 30 OR Population standard deviation σ is given then We use Z test.

If sample size n < 30 AND Population standard deviation σ is unknown then we use t test.

In this question we are not given Population standard deviations σ1 and σ2.

Also n1 = 14 and n2 = 13 both sample sizes are LESS than 30.

Therefore we use t test.

Given :- Assume the population standard deviations are equal. ( σ1 = σ2)

then Degrees of freedom = n1 + n2 - 2 = 14 + 13 - 2 = 25.

(kindly find the image attached with this solution)

Answer :- Therefore 25 degrees of freedom are used to find the t critical value.

5 0

3 years ago

Anne has three more dollars than Freddy. Together they have $99. How many dollars does each have?

Tamiku [17]

Anne has 51. Freddy has 48.

7 0

3 years ago

Read 2 more answers

Combine the following sets of terms.

DanielleElmas [232]

Let's simplify step-by-step To understand :)

3x2−7x−(x2+3x−9)

Distribute the Negative Sign:

=3x2−7x+−1(x2+3x−9)

=3x2+−7x+−1x2+−1(3x)+(−1)(−9)

=3x2+−7x+−x2+−3x+9

Combine Like Terms:)

=3x2+−7x+−x2+−3x+9

=(3x2+−x2)+(−7x+−3x)+(9)

=2x2+−10x+9

Answer :)

=2x2−10x+9

HOPE THIS HELPS

3 0

3 years ago

The sum of two numbers is 30. the first number is 1/5 of the second number. what are the numbers?

bonufazy [111]

Same question
x+y=30
x is 1/5 of y
x=y/5
subsitute
y/5+y=30
multily both sidse by 5
y+5y=150
add
6y=150
divide both sides by 6
y=25
subsitute
x=y/5
x=25/5
x=5
the numbers are 5 and 25

6 0

3 years ago