Paul drives his delivery van 675 miles in 3 days. at this rate, how far will he drive in 15 days?
a. 45 miles
b. 225 miles
c. 2,025 miles
d. 3,375 miles

As per the unitary method, the number would you expect to be confirmed for MDD at the follow-up visit is approximately 166.

The term unitary method in statistics refers a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have to find how many of your 500 clients would you expect to have major depressive disorder and  if you used the phq-2 to screen for MDD, what number of those who are depressed would screen positive.

In order to find the number of patients with MDD, we must know the process of PHQ - 2.

The process of PHQ - 2 involves the following steps:

Here the score ranges from 0-6.

And if the score is 3 or greater, then major depressive disorder is likely.

Based on these we have to test the 500 with PHQ test, let us consider that there is 2 person in every two person has MDD.

So, the number of MDD patient is approximately 166.

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Given the prime factorization of 90. The number that complete thi prime factorization is 2 × 3² × 5.

Factor tree

  90

   /\

2  45

     /\

  3  15

       /\

    3   5

The prime factorization

90 = 2 × 3 × 3 × 5

     = 2 × 3² × 5

So, the number that complete thi prime factorization is 2 × 3² × 5.

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To find the time and distance at which Liza passes Ralph, we need to solve the system of equations.

Subtracting the first equation from the second, we get:

65x - 60x = y - 25

5x = y - 25

y = 5x + 25

Substituting this value of y into the first equation, we get:

60x + 25 = 5x + 25

55x = 0

x = 0

This means that Liza will pass Ralph 0 hours after she leaves, or at the same time as Ralph. At this time, they will have both traveled 0 miles.

Therefore, the answer is A: Liza will not pass Ralph, because she will never catch up with him.

Answer:

2,3 and 7

Step-by-step explanation:

168 = 2x2x2x3x7

= 2²x3x7

The percent increase  from last year to this year is 7.94%

From the question, we have the following parameters that can be used in our computation:

Initial height = 63 inches

New height = 68 inches

The percent change from last year to this year is then calculated as

Percent change = (New height - Initial height)/Initial height * 100%

Substitute the known values in the above equation, so, we have the following representation

Percent change = (68 - 63)/63 * 100%

Evaluate

Percent change = 7.94%

Hence, the percentage increase is 7.94%

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Answer:

Negative

Step-by-step explanation:

Knowledge Needed

The discriminant of a quadratic function is b^2-4ac.

If the discriminant is positive, there are 2 x-intercepts.

If the discriminant is 0, there is 1 x-intercept.

If the discriminant is negative, there are 0 x-intercepts.

Question

If the parabola does not intersect with the x-intercept, the discriminant is negative.

Answer:

To find the area of a triangle, we can use the formula:

Area = (base * height) / 2

To find the area of triangle ABC, we first need to find the base and the height.

Since angle B is 75 degrees, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle A: 180 - 75 - 90 = 15 degrees.

Then, we can use the fact that the measure of an angle in a triangle is proportional to the length of the side opposite that angle to find the length of side AC:

AC/AB = m∠A/m∠B

AC = (m∠A/m∠B) * AB

Substituting, we get:

AC = (15/75) * 12 = 3

Now that we know the base and the height of the triangle, we can use the formula to find the area:

Area = (3 * 12) / 2 = 18

Therefore, the area of triangle ABC is 18 square cm.

The proportionality used in the given diagram is 4/3=12/x if ΔABC and ΔDEF are similar. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

We have to assume that ΔABC and ΔDEF are similar.

If the triangles are similar,

Then the proportionality is:

AB/BC=DE/EF

4/3=12/x

Therefore, the proportionality used in the given diagram is 4/3=12/x.

So, option 4 is correct.

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The equation that represents the number of time a cricket chirp (y) given the temperature (x) in degree Fahrenheit is y = 0.23 x + 40

Steps to translate a word problem into an equation or a function:

- Assign the unknowns to variables

- Identify which one is independent variables, which one is dependent variables. The independent variable will become the input while the dependent variable will become the output.

In the given problem, there are two variables:

- temperature in the air (in Fahrenheit)

- number of time a cricket chirp

From the problem, we can conclude that the number of time a cricket chirp depends on the temperature of the air. Hence,

independent variable =  temperature in the air (in Fahrenheit)

dependent variable = number of time a cricket chirp

Let:

y =  number of time a cricket chirp

x =  temperature in the air (in Fahrenheit)

It is said: The number of chirp per minute is equal to 0. 23 times the temperature of the air, in degree Fahrenheit, plus forty.

We can translate it into an equation:

y = 0.23 x + 40

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The required values of the z-score as per the corresponding blood pressure readings are: z-score = 1.267 when reading is 142, z-score = 0.6 when reading is 130, and z-score = -1.2- when reading is 103.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

Normally distributed with a mean of 121 and a standard deviation of 15.

As per the given question, we have

mean ц = 121

standard deviation σ = 15

For X₁ = 140

z-score = (X₁ - ц )/σ

z-score = (140 - 121)/15

z-score = (19)/15 = 1.267

For X₂ = 130

z-score = (X₂ - ц )/σ

z-score = (130 - 121)/15

z-score = (9)/15 = 0.6

For X₃ = 103

z-score = (X₃ - ц )/σ

z-score = (103- 121)/15

z-score = (19)/15 = - 1.2

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Divide by 12 to go from the APR to the monthly interest rate

(9.5%)/12 = 0.7916667%

The decimal form is 0.007916667 approximately.

Multiply this with the starting balance $1367.90 and we get:

0.007916667*1367.90 = 10.8292 which rounds to 10.83

The interest payment for the 1st month is $10.83; which means the principal payment would be 400-10.83 = 389.17

This principal payment will then drop the balance from $1367.90 to 1367.90-389.17 = 978.73 dollars.

The value $978.73 is now the starting balance of the 2nd month. This process of...

is repeated until the balance is $0.

This is what the table would look like

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6}\text{Month} & \text{Starting} & \text{Interest} & \text{Principal} & \text{Payment} & \text{Ending }\\& \text{Balance} & & & & \text{Balance}\\\cline{1-6}1 & 1367.9 & 10.83 & 389.17 & 400 & 978.73\\\cline{1-6}2 & 978.73 & 7.75 & 392.25 & 400 & 586.48\\\cline{1-6}3 & 586.48 & 4.64 & 395.36 & 400 & 191.12\\\cline{1-6}4 & 191.12 & 1.51 & 191.12 & 192.63 & 0\\\cline{1-6}\end{array}[/tex]

Many credit card companies and banks offer free calculators on their website, or you can find similar free calculators online elsewhere, that will quickly calculate a table like shown above. It is called an amortization table or amortization schedule.

With the exception of the 4th month, each row has the principal and interest add to the $400 monthly payment. The last row will have a payment of 1.51+191.12 = 192.63 dollars.

The total amount paid back would be 400+400+400+192.63 = 1392.63 dollars. This is the sum of the values in the "payment" column.

-------------------------------------------------------------------------

Here's another way to determine the answer.

The monthly payment formula is

[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}[/tex]

where,

In this case,

Let's solve for the variable n. We'll need logarithms to isolate the exponent.

Part 1

[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}\\\\\\\displaystyle 400 = \frac{1367.90*0.007916667}{1 - (1+0.007916667)^{-n}}\\\\\\\displaystyle 400 = \frac{10.8292087893}{1 - (1.007916667)^{-n}}\\\\\\\displaystyle 400(1 - (1.007916667)^{-n}) = 10.8292087893\\\\\\[/tex]

Part 2

[tex]\displaystyle 1 - (1.007916667)^{-n} = 10.8292087893/400\\\\\\\displaystyle 1 - (1.007916667)^{-n} = 0.0270730\\\\\\\displaystyle -(1.007916667)^{-n} = 0.0270730-1\\\\\\\displaystyle -(1.007916667)^{-n} = -0.9729270\\\\\\\displaystyle (1.007916667)^{-n} = 0.9729270\\\\\\[/tex]

Part 3

[tex]\displaystyle \log((1.007916667)^{-n}) = \log(0.9729270)\\\\\\\displaystyle -n*\log(1.007916667) = \log(0.9729270)\\\\\\\displaystyle n = -\log(0.9729270)/\log(1.007916667)\\\\\\\displaystyle n = 3.4805965\\\\\\[/tex]

Each decimal value is approximate.

That value of n then rounds up to the nearest integer n = 4

We do not round to n = 3 since that would be one month short, as shown in the table above.

You can use a graphing calculator to quickly solve that equation for the variable n. It can be used as a way to visually confirm the answer.

To find the total mass of all the worker bees in the hive, you need to multiply the mass of a single worker bee by the number of worker bees in the hive.

The mass of a single worker bee is 2 x 10^-4 kilograms, and there are 8 x 10^4 worker bees in the hive.

So the total mass of all the worker bees in the hive is (2 x 10^-4 kilograms) * (8 x 10^4 worker bees) = 0.16 kilograms.

In standard form, this is written as 1.6 x 10^-1 kilograms.

Answer:

Step-by-step explanation:

Answer is B.

Function 1: slope is 2

Function 2: (-5 + 4)/(2-1)= -1/1= -1

Option B is the correct answer. corresponding sides have a proportional ratio is 1/3 of the sss theorem.

If two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. This is called the SSS Similarity Theorem.

when the three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar, it is also called SSS Similarity Theorem.

SSS Theorem png

If  ABYZ=BCZX=ACXY , then ΔABC∼ΔYZX .

Considering triangles have 3 sides, having each side has a 1/3 ratio will make it congruent to the other triangle.

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Answer:

Step-by-step explanation:

If the car holds at most 14.5 gallons of gas and you use 1.5 gallons of gas on the way to the grocery store, the amount of gas you have left in your tank can be represented by the inequality:

[tex]14.5 - 1.5 < = x[/tex]

This inequality can be read as "14.5 minus 1.5 is less than or equal to the amount of gas you have left in your tank, x."

Solving for x, we get:

[tex]x > = 13[/tex]

So the amount of gas you have left in your tank is greater than or equal to 13 gallons.

Answer:

maybe 16

I hope I helped

Step-by-step explanation:

joining m < 5 = m < 7

8x – 14 = 5x + 34

8x – 5x = 34 + 14

3x = 48

divide both sides by 3

x = 48/3

x = 16

The linear equation that represents the plant height is the one in the first option:

y = 14 + (3/2)x

We know that the initial height of the plant (this will be the y-intercept of the line) is 14cm, and we also know that the plant grows at a rate of 3/2 cm each day.

So, after x days, the plant is x times 3/2cm plus 14 cm of height, so the linear equation is:

y = 14 + (3/2)x

So the correct option is the first one.

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Answer:y=7.5x

Step-by-step explanation:

In the 9th grade HMH Math book for teachers, it explains that you must divide 150 by 20 and put it in the equation.

In terms of b, the perimeter expression is 6 + 4b and the value of b is 9

From the question, we have the following parameters that can be used in our computation:

Dimensions = 8cm and 2b - 5 cm

The above parameters mean that

Length = 8

Width = 2b - 5

The perimeter is calculated as

Perimeter = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (8 + 2b - 5)

Evaluate the like terms

Perimeter = 2 * (3 + 2b)

Open the brackets

Perimeter = 6 + 4b

Here, we have

Perimeter = 42

This means that

6 + 4b = 42

So, we have

4b = 36

Divide by 4

b = 9

Hence, the value is 9

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Answer:4c=h

Step-by-step explanation:

The first linear equation, 4c=h

The team of Rosie's Riveters beat the Susan Bees by 3 runs.

Given are the scores for two softball teams for seven innings.

The total score of Rosie's Riveters will be -

T{R} = 1 + 3 + 4 + 2 + 1 + 0 + 2 = 13

The total score of Susan Bees will be -

T{S} = 0 + 0 + 5 + 3 + 0 + 1 + 1 = 10

Now -

T{R} - T{S} = 13 - 10 = 3

T{R} - T{S} = 3

Therefore, the team of Rosie's Riveters beat the Susan Bees by 3 runs.

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Answer:

slope = 6

Step-by-step explanation:

(0,6)
(1,12)

12-6

-------- = 6

1-0

The point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].

To find the tangent of a curve, we have to find the first derivative of the function. Hence, the tangent of the given curve is given by

⇒ [tex]f'(x) = \frac{d{f(x)}}{dx} = \frac{d{x^{2}}}{dx} + \frac{d(4x)}{dx} - \frac{d(1)}{dx}[/tex]

⇒ [tex]f'(x) = 2x + 4[/tex]

Now, as the tangent is horizontal, that means the slope of the tangent is 0, hence setting [tex]f'(x) = 0[/tex] , we get the equation

⇒ [tex]f'(x) = 2x + 4 = 0[/tex]

Solving the equation obtained for the variable x,

⇒ [tex]2x = -4\\[/tex]

⇒ [tex]x = -2[/tex]

Now, putting the obtained value for x in the original equation, we get

⇒ [tex]f(x) = (-2)^{2} + 4(-2) - 1\\[/tex]

⇒ [tex]f(x) = -5[/tex]

Hence, the point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].

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Answer:

4×-4y=4

-(4x+y=19)

0x -5y=-15

5y=15

y=3

4x-12=4

x=4

Step-by-step explanation:

1.

it is always the same.

the usual equation of a line is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y-value when x = 0).

we see that the y-value is +3 when x = 0. that is "b".

for the slope we pick 2 points (with integer coordinates, if possible).

I see e.g. (0, 3) and (3, 0)

x changes by +3 (from 0 to 3).

y changes by -3 (from 3 to 0).

the slope "a" is -3/+3 = -1

the equation is

y = -x + 3

2.

and again the same

we see that the y-value is -3 when x = 0. that is "b".

I see e.g. (0, -3) and (3, 0) as points.

x changes by +3 (from 0 to 3).

y changes by +3 (from -3 to 0).

the slope "a" is +3/+3 = 1.

the equation is

y = x - 3

The probability of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

It is represented mathematically as;

Probability = Number of Expected outcomes / Total number of outcomes

From the question, we can have the following outcomes;

Clothing = 4

Colors = 3

Pr (pick a clothing) = 1/4

Pr (pick a color) = 1/3

Pr (picking an orange hat) = 1/4 x 1/3

Pr (picking an orange hat) = 1/12.

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Answer: Sofia needs to order an additional 100 - 24 = 76 pieces of sushi.

Since each roll contains 12 pieces, Sofia needs to order 76 / 12 = 6 additional rolls of sushi.

At a cost of $8 per roll, Sofia will need to pay an additional 6 * $8 = $48 for the additional sushi.

Step-by-step explanation:

Answer:

let x as hotdog and x + 42 as soda

x + x + 42 = 250

2x + 42 = 250

2x + 42 - 42 = 250 - 42

2x = 208

x = 104

sodas sold: x + 42 = 104 + 42 = 146 sodas

hotdogs sold: x = 104 hotdogs

Step-by-step explanation:

Answer:

104 hot dogs sold

146 sodas sold

Step-by-step explanation:

s=number of sodas. h=number of hotdogs

s+h=250

s=h+42  ==> there were 42 more sells for soda than compared to hot dog

h+42+h=250  ==> plugin h+42 for s

h+h+42=250 ==> simplify

2h+42=250 ==> solve for h

2h+42-42=250-42 ==> isolate h by subtracting 42 on both sides

2h = 208

h = 208/2

h = 104 hot dogs sold

s=104+42  ==> plug in 104 for h in s=h+42

s = 146 sodas sold