The sum of four consecutive odd integers is 136. What are the four integers

Marco does 14 extra math problems each school night how many extra problems does he do each week. there are 5 school nights in a

Alexus [3.1K]

Marco does 70 extra math problems each week. 14(5)=70

4 0

2 years ago

Read 2 more answers

A function is given. h(t) = t2 + 3t; t = −1, t = 2

Arlecino [84]

Answer:

(a) The net change of the function is 12.

(b) The average rate of change of the function 4.

Step-by-step explanation:

The average rate of change of function $f(x)$ over the interval $a\leq x\leq b$ is given by this expression:

average rate of change = $\frac{net \:change \:in \:y}{change \:in \:x} = \frac{f(b)-f(a)}{b-a}$

It is a measure of how much the function changed per unit, on average, over that interval.

Given:

$h(t)=t^2+3t\\\\t=-1\\t=2$

(a) To find the net change of the function, first we calculate the values of $h(2)$ and $h(-1)$

$h(-1)=(-1)^2+3(-1)=-2\\\\h(2)=(2)^2+3(2)=10$

The net change is simply the difference

$h(2)-h(-1)=10-(-2)=12$

(b) The average rate of change takes the net change and divides it by the change in the $t$ value.

$\frac{12}{2-(-1)} =\frac{12}{3}=4$

5 0

3 years ago

Read 2 more answers

Solve the equation for all values of x.<br> (8x+9)(49x^2-100)=0

Liono4ka [1.6K]

Answer:

$x = \frac{-9}{8} , \frac{-10}{7} , \frac{10}{7}$

Step-by-step explanation:

8x+9=0

8x=-9

$x = \frac{-9}{8}$

or

$49x^{2}-100 = 0$

$(7x)^{2} -10^{2} =0$ ,

$(7x+10)(7x-10)=0$

$7x+10=0, 7x-10=0$

$7x=-10, 7x=10$

$x=-\frac{-10}{7}$ , $x = \frac{10}{7}$

4 0

2 years ago

Answer the original questions. (2 points: 1 point ea a) How long is each individual act? b) How long is each group act

Rufina [12.5K]

Answer:

a) Each individual act will last 5 minutes.

b) Each group act will last 10 minutes.

Step-by-step explanation:

I think this is right

5 0

2 years ago

150 students were surveyed on how many text messages to send in a date for different devices. let X represent the number of stud

kakasveta [241]

Given that the total number of students that sent messages = 150 students

a) To obtain the equation to represent the number of students who send text messages, we will sum up the variables in the Venn diagram and equate it to 150.

$\begin{gathered} 75+x+3x+x=150 \\ x+3x+x=150-75 \\ 5x=75 \end{gathered}$

Hence, the equation is

$5x=75$

b) Solving for x

$\begin{gathered} 5x=75 \\ x=\frac{75}{5}=15 \\ \therefore x=15 \end{gathered}$

Therefore, x = 15.

c) The total number of student that uses cell phone = 75 + x = 75 + 15= 90students

The total number of students that sent messages = 150students

The formula for probability is,

$\text{Probability = }\frac{\text{Number of students that uses cell phone}}{\text{Total number of students}}$

Hence,

$P(\text{Number of students that uses cell phone)}=\frac{90}{150}=\frac{3}{5}$

Therefore, the probability that a randomly chosen student uses their cell phone to send text messages is 3/5.

7 0

1 year ago