Given two points on a line (2, 5) and (6, 11), what is the rate of change?

Toby invested £7500 for 2 years in a savings account. he was paid 4% per annum compound interest. how much money did Toby have a

Oduvanchick [21]

A=7,500×(1+0.04)^(2)
A=8,112

7 0

3 years ago

Lindsay is creating a bridge out of dried pasta and glue. In her plans, she sketches the graph to determine the lengths of the n

alexgriva [62]

From the graph shown it can be seen that the bridge is represented by a parabola with vertex of (5, 8) and roots of 1 and 9.

Recall that the vertex form of the equation of a parabola with vertex (h, k) is given by
$y=a(x-h)^2+k$

Thus, the equation of the given graph in vertex form is given by
$y=a(x-5)^2+8$

Also, recall that the equation of a parabola with roots, p and q, is given by
$y=a(x-p)(x-q)$

Thus the equation of the given graph can be given by
$y=a(x-1)(x-9)$

To get the value of a, we equate both equations and solve as follows:
$a(x-5)^2+8=a(x-1)(x-9) \\ \\ a(x^2-10x+25)+8=a(x^2-10x+9) \\ \\ ax^2-10ax+25a+8=ax^2-10ax+9a \\ \\ 25a-9a=-8 \\ \\ 16a=-8 \\ \\ a=- \frac{8}{16} =- \frac{1}{2}$

Therefore, the function that Lindsay used to create her design is
$f(x)=-0.5(x-5)^2+8$

4 0

3 years ago

Read 2 more answers

Write the converse of this conditional statement If an animal is a poodle, then it is a dog.

Llana [10]

Answer:

It's a dog of an animal is a poodle.

Step-by-step explanation:

You switch the order of the statement.

5 0

2 years ago

100 students went on a field trip. 6 buses were filled and 10 students traveled to the destination in cars with their parents. H

mars1129 [50]

Answer:

15 students were on each bus.

Step-by-step explanation:

100 students have gone a field trip, 10 have travelled with their parents. So, you would do 100-10 to get 90. 90 students are riding the buses. To get the amount of students on each buses, you have to do 90÷6 to get 15.

8 0

3 years ago

Esearchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of

Dovator [93]

Answer:

The correct option is (D).

Step-by-step explanation:

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard H₀.

A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The hypothesis is defined as follows:

H₀: The slope of the regression line is 0, i.e. β = 0.

Hₐ: The slope of the regression line is greater than 0, i.e. β > 0.

A scatter-plot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables; lean body mass and maximal oxygen uptake.

The significance level of the test is, α = 0.05.

The p-value of the test is, p-value = 0.04

As the p-value = 0.04 < α = 0.05, we reject the null hypothesis.

So, it can be concluded that there is a statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes.

Since the scatter-plot shows a strong positive linear relationship, it implies that as the an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes.

Thus, the correct option is (D).

7 0

3 years ago