Does the shape below show a correct line of symmetry

Doss [256]

9/13 is thw answereto

6 0

3 years ago

The sum of an arithmeit cprogression consisting of 20 positive integer terms with positive common difference is equal to 2020. (

Rufina [12.5K]

Answer:

a) possible progressions are 5

b) the smallest and largest possible values of the first term are 16 and 82

Step-by-step explanation:

Sum of terms:

Sₙ = n/2(a₁ + aₙ) = n/2(2a₁ + (n-1)d)
S₂₀ = 20/2(2a₁ + 19d) = 10(2a₁ + 19d)
2020 = 10(2a₁ + 19d)
202 = 2a₁ + 19d

In order a₁ to be an integer, d must be even number, so d = 2k

202 = 2a₁ + 38k
101 = a₁ + 19k

Possible values of k= 1,2,3,4,5

k = 1 ⇒ a₁ = 101 - 19 = 82
k = 2 ⇒ a₁ = 101 - 38 = 63
k = 3 ⇒ a₁ = 101 - 57 = 44
k = 4 ⇒ a₁ = 101 - 76 = 25
k = 5 ⇒ a₁ = 101 - 95 = 16

As per above,

a) possible progressions are 5
b) the smallest and largest possible values of the first term are 16 and 82

6 0

3 years ago

A bike rental shop rents out bicycles with a flat rate of $6 and then charges $2 per hour a person rents out the bike. Identify

DIA [1.3K]

Answer:

Independent Variable: Number of hours

Dependent Variable: Cost

Equation: C = 2x + 6

Step-by-step explanation:

The independent variable (x) is the variable that is manipulated. In this instance, that would be the number of hours a person rents out the bike.

The dependent variable (C) is the variable that is manipulated depending on the value of the independent variable. In this instance, that would be the total cost for renting the bike.

The total equation would be C = 2x + 6. The coefficient, 2, represents the charge of $2 per hour and the 6 represents the starting charge of $6.

6 0

3 years ago

Explain how you could mentally find 8x45by using the distributive property

777dan777 [17]

You just break it up, do 20x8 then another 20x8 then 5x8

7 0

3 years ago

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of t

ivolga24 [154]

Answer:

$p_v =P(t_{(29)}>1.42)=0.0831$

For this case the p value calculated is higher than the significance level used of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case would be:

a) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

Step-by-step explanation:

Information given

We want to verify if he mean IQ of employees in an organization is greater than 100 , the system of hypothesis would be:

Null hypothesis: $\mu \leq 100$

Alternative hypothesis: $\mu > 100$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic calculated for this case $t_{calc}= 1.42$

The degrees of freedom are given by:

$df=n-1=30-1=29$

Now we can find the p value using tha laternative hypothesis and we got:

$p_v =P(t_{(29)}>1.42)=0.0831$

For this case the p value calculated is higher than the significance level used of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case would be:

a) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

5 0

3 years ago