twice the larger of 2 consecutive integers equal 15 less than 3 times the smaller

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

∠PML = 140°

∠KHP = 20°

We need to find the measure of ∠PHJ.

Let m ∠PHJ = x°

From the graph, we conclude that

∠PML = ∠PHJ + ∠KHP (Vertically opposite angle)

[tex]140^\circ=x+20^\circ\\\\140^\circ-20^\circ=x\\\\120^\circ=x[/tex]

Hence, Option 'B' is correct.

Yes, this relationship is proportional.

Answer:

Yes, the relationship is proportional

Step-by-step explanation:

This is because the number of hours (x) is multiplied by the same number, 7.5, meaning that all of the values will be proportional (create a straight/linear line on a graph when the points are plotted).

First, we would set the number to x.

Then, we turn the words into an equation.

x+75 = 3x-39

Isolate the x.

-2x = -114

So...

x = 57

The Number is 57.

Let's call the number you're trying to find "x."

According to the information given, if 75 is added to x, the result is 39 less than three times the number, which can be expressed as:

x + 75 = 3x - 39

To solve for x, you can first get all the x terms on one side of the equation and the constant terms on the other side:

75 + 39 = 3x - x

Now, simplify the equation:

114 = 2x

To isolate x, divide both sides by 2:

x = 114 / 2

x = 57

For more such questions on Number

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(- 3, ∞ )

the parenthesis at both ends indicates x ≠ - 3 or ∞

if x ≥ - 3 then {- 3, ∞ )

the square bracket on the left indicates x can equal - 3

Final answer:

The inequality x > -3 in interval notation is (-3, ∞), which means that the solution set for x includes all values greater than -3, but does not include -3 itself.

Explanation:

When the inequality x > -3 is written in interval notation, it means that the solution set for x includes all values greater than -3, but does not include -3 itself. In interval notation, we use a round bracket to indicate that -3 is not included in the solution set. The interval notation for x > -3 is (-3, ∞). This notation represents a half-open interval, where -3 is excluded but all values greater than -3 are included. The symbol ∞ represents infinity, indicating that there is no upper bound for the values of x in this inequality.

Answer:

Cutoff for a failing score is 49 and 2.28% students failed.

Step-by-step explanation:

We have been given that scores on a psychology exam were normally distributed with a mean of 57  and a standard deviation of 4.

2 standard deviation below mean would be,

[tex]57-2(4) =57-8= 49[/tex]

Therefore,Cutoff far a failing score is 49.

Now let us find out the z-score for our given values,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{49-57}{4}=\frac{-8}{4} =-2[/tex]

Now let us look up the probability from normal distribution table.

[tex]P(z<-2) =0.02275[/tex]

Therefore, percentage of students failed is 2.28%.

the slope is 3/-5!!!! if u go up 3 and to the LEFT 5 that means it is negative.

she will need to mow 8 yards because 109 divided by 15 equals 7.2 but she cant just mow 7.2 yards so you round up to 8 yards

The unit rate is $/Hr.  Since the hours are the unit being considered.

To find the unit rate, divide both sides by three

(Let x = hourly rate)

3x = 15

x = 5

Miguel Makes $5 per Hour

Answer:

He Earns 5 Per Hour

3(x-2)+5x=18

the correct answer is x=3

first simply the equation

8x=18+6

Now rid of alike terms resulting in

8x=24

now divide 24 by 8

x=3

the volume (V ) of a cuboid is V = Ah

where A is the area of the base or top and h is the height

h = 180 cm = 1.8m

V = 0.6 × 1.8 = 1.08 m³

The volume of the refrigerator is calculated by converting its height from centimeters to meters (180 cm = 1.8 m) and then multiplying it by the given area of the top (0.6 m²), resulting in a volume of 1.08 cubic meters.

To calculate the volume of the refrigerator, we need to use the formula for the volume of a rectangular prism, which is Volume = length x width x height. We already have the area of the top of the refrigerator, which is a product of its length and width, and we're given the height. However, firstly we need to ensure that all units are in meters.

Convert the height from centimeters to meters: 180 cm = 1.8 m.

Now, we can calculate the volume: Volume = Area x Height = 0.6 m² x 1.8 m = 1.08 m³.

Therefore, the refrigerator has a volume of 1.08 cubic meters.

x = 21

y = 6

x = 4y - 3

x + y - 7 = 20

Because we have a value for x, we can put it in the second equation to find the value of y.

4y - 3 + y - 7 = 20

Combine like terms.

5y - 10 = 20

Add 10 to both sides.

5y = 30

Divide both sides by 5.

y = 6

Now we can place this value of y back into the equation to find the exact value of x.

x + 6 - 7 = 20

Combine like terms.

x - 1 = 20

Add 1 to both sides.

x = 21

The answer is C,

200 is the original distance

plus the increasing 5 yards everyday

The expression y = kx can be used to find the value of y when x is given. In this case, the value of y when x is 2 is 16.

To find the expression to determine the value of y when x is 2, we need to use the fact that y varies directly as x. This can be represented by the equation y = kx, where k is the constant of variation.

We are given that when x is 6, y is 48. Plugging these values into the equation, we have 48 = k * 6. Solving for k, we find that k = 8.

Now we can use this value of k in our equation to find y when x is 2. Substituting 8 for k and 2 for x, we have y = 8 * 2 = 16. Therefore, the value of y when x is 2 is 16.

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Question says that a yogurt shop allows its customers to add, for no charge, 3 toppings to any yogurt purchased. Also the store has 15 possible toppings.

Now we need to find about how many different 3-topping combinations can a customers choose.

To find that we just need to apply combination formula

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

which is used to select r items out of n items

we have to find combination of 15 toppings into 3 toppings so we calculate C(15,3) using above formula

[tex]C(15,3)=\frac{15!}{3!(15-3)!}[/tex]

[tex]C(15,3)=\frac{15!}{3!*12!}[/tex]

[tex]C(15,3)=\frac{15*14*13*12!}{3!*12!}[/tex]

[tex]C(15,3)=\frac{15*14*13}{3!}[/tex]

[tex]C(15,3)=\frac{2730}{6}[/tex]

[tex]C(15,3)=455[/tex]

Hence final answer is 455.

Answer:

only 455

Step-by-step explanation:

i have a ? how do you know when its C(n,r) and not P(n,r)

Answer:

Anna is 41 years old.

Step-by-step explanation:

Easiest way to do this is by building a equation,

Lest say Anna's age is [tex]x[/tex].

Then as Peter is 3 years older than Anna Peter's age should be [tex]x+3[/tex].

Then the combined ages of the two people is given as 85. So we can write an equation as,

[tex]x+(x+3)=85[/tex]

[tex]x+x+3=85[/tex]

[tex]2x+3=85[/tex]

[tex]2x+3-3=85-3[/tex] (deducting 3 from both sides of the equation)

[tex]2x=82[/tex]

[tex]x=41[/tex]

As we originally took Anna;s age as [tex]x[/tex]

We can say Anna is 41 years old.

When changing a repeating decimal to a fraction, you look at the number(s) to the right of the decimal. If there is only 1 number (0.444444...) then the number that repeats is is going to be the numerator of your fraction, with the denominator being 9 (4/9). So...

1. -1 2/9 (-1 and 2/9)

2. -5/9

5. 5 8/9 (5 and 8/9)

If there are 2 or more numbers to the right of the decimal, you add 1 "9" to the denominator per repeating number (2 repeating numbers = 99, 3 repeating numbers = 999, etc...). An example to show this would be 0.87 repeating (0.87878787... = 87/99). Therefore...

3. 27/99

4. 50/99

I hope this helps!

6•50=$3.00 pennies

5•40=$2.00 nickels

50•10=$5.00 dimes

25•40=$10.00 total $20.00

Answer: $63

Step-by-step explanation:

Penny = $0.01

Nickel = $0.05

Dime = $0.1

Quarter= $0.25

Number of pennies = 6(50) = 300

Number of nickels = 5(40)= 200

Number of dimes = 4(50)= 200

Number of quarters = 3(40) = 120

Total amount of money:

300(0.01)+ 200(0.05) + 200(0.1) + 120(0.25) = $63

Answer:

The correct option will be:  B) 2,500

Step-by-step explanation:

Nikita invest 2000 into a bank account with a 4% annual interest rate.

So, the amount of interest in one year will be:  [tex](2000*0.04)= 80[/tex]

and the amount of interest in 7 years will be: [tex](80*7)=560[/tex]

Thus, the total money in her account after 7 years [tex]=(2000+560)=2560[/tex]

So, the most expensive item she can afford to buy will be:  2500

Answer:

The answer is (a mountain bike priced at $2,500) In Plato

Step-by-step explanation:

- 3 1/2 = 2x

-7 /2   = 2 x

-7 /4  = x

-1 3/4 = x

AC = CB, hence ΔABC is isosceles

the base angles 34 and x - 5 are therefore equal

x - 5 = 34 ( add 5 to both sides )

x = 39

and 4y = 180 - ( 2 × 34 ) = 112

4y = 112 ⇒ y = 28

Answer:

x=39° ,y=28°

Step-by-step explanation:

In the given figure

Side AC = Side BC

Hence ΔABC is an isosceles triangle.

⇒∠CAB =∠CBA   (∵ angles  opposite to equal sides are equal)

                        ⇒  (x - 5)° = 34°  

                            ⇒  x = 39

Also in Δ ABC

            ∠ABC + ∠ACB + ∠CAB = 180°

                                                    (∵ Sum of all the interior angles of a triangle)

               ⇒   34° + 34° + 4 y = 180°

                 ⇒     4 y =180°-68°

                    ⇒     y=112°÷ 4

                        ⇒y= 28°

Hence, x = 39° , y = 28°

The graph of the line would get less steep.

(APEX approved~)

Answer:

D) Less steep.

[tex]|-2 + (-1)|[/tex]

Well, first, we must subtract-2 by 1, as the negative sign next to 1 is inside the parentheses.

[tex]|-2 -1|[/tex]

[tex]|-3|[/tex]

Now remember, since it is an absolute value, meaning the distance from that number to zero, we will now disregard the negative sign and get our answer: 3

Method One:

Step One: Figure out how long the width is, witch is 19 feet.

Step Two: Multiply 2*19 and 3*11 because it is 2 times as long and three times as wide

Step Three: Add 38+33

The new perimeter will be 71 feet.

The original garden's width is determined to be 4 feet. Upon expanding the garden to triple its length and double its width, the new garden's perimeter is calculated to be 82 feet.

The question is about calculating the perimeter of a new garden based on given dimensions and scale factors for its expansion. The original garden has a perimeter of 30 feet and a length of 11 feet. To find the width, we use the formula for the perimeter of a rectangle, P = 2l + 2w, which gives us 30 = 2(11) + 2w. Solving for w, we find that the width of the original garden is 4 feet.

Given that Mr. Glidden is expanding his garden to be 3 times as long and 2 times as wide, the new dimensions will be 3(11) feet by 2(4) feet, or 33 feet by 8 feet.

Therefore, the new perimeter will be 2(33) + 2(8), which equals 66 + 16, resulting in a new perimeter of 82 feet.

38.9e i think 60% sure