What expression is five times the sum of two numbers

Average cost = Total cost / Number of supplies

The cost of the present is $20.67

Given,

The cost of the present = x

Amount given by cousin = $13.78

Amount given by cousin is 2/3 of x.

That is,

13.78 = 2/3 of x

Lets find x

13.78 = 2/3 × x

13.28 = 2x/3

Multiply with 3 on both sides

13.78 × 3 = (2x/3) × 3

We get,

41.34 = 2x

Divide 2 on both sides

That is,

41.34/2 = 2x/2

We get,

x = 20.67

Here, x is the cost of the present

Therefore, the cost of the present is $20.67

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9514 1404 393

Answer:

  "and"

Step-by-step explanation:

Properly written, the word "and" separates the integer portion from the fractional portion of the number. If there is no "and", then there is no integer portion, so the number is a fraction less than 1.

Examples:

one and three tenths = 1 3/10

thirty-one thousandths = 31/1000

The amount of wax needed to make 288 candles is  41472 inches³.

A company makes wax candles in the shape of a rectangular prism. Each candle is 6 inches long, 3 inches wide, and 8 inches tall.

Therefore, the amount of wax to make 288 candles can be calculated as follows:

Hence,

volume of each rectangular prism = 6 × 3 × 8

volume of each rectangular prism = 18 × 8

volume of each rectangular prism = 144 inches cube

Therefore,

1 candle =  144 inches cube

288 candles = ?

cross multiply

volume of wax for 288 candles = 288 × 144

volume of wax for 288 candles = 41472 inches³

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Answer:

The 3rd option would be correct

Step-by-step explanation:

4 is the starting point (b) and 4/3 is the slope (m) hope this helps! Plzz mark brainliest

Answer:

B (-7, 1)

Step-by-step explanation:

All we have to do is set up equations to find coordinate b from midpoint formula.

x-coordinate:

-2 = \(\frac{3+x}{2}\)

-4 = 3 + x

x = -7

y-coordinate:

3 = \(\frac{5+y}{2}\)

6 = 5 + y

y = 1

Given that

The figure is given on the coordinate plane. And we have to find the vertices of the figure after a 90-degree clockwise rotation.

Explanation -

So the figure will be rotated from its position clockwise as

Since the given points are J(-9, -8)

K(-2, -8)

L(-2, -3)

M(-9, -3)

After rotating the points will be

J(

K(-7, -3)

L(-2, -3)

M(-2, 4)

Answer: 8 and 0.6666

4 times 2: Count by twos four times to get 8.

Divide 2 by 3: think about if 2 can go into 3. Since 3 is bigger than 2 you have to add a zero to the end of two to make it 20. 3 can go into 20 six times. It should be a repeating decimal.

Answer:

  (d)  240/289

Step-by-step explanation:

The trig identity for the sine of a double angle can be used to find the desired value.

  sin(2θ) = 2sin(θ)cos(θ)

__

The cosine of this 3rd-quadrant angle is negative:

  cos(θ) = -√(1 -(-8/17)²) = -(√(289 -64))/17 = -15/17

Then the desired sine value is ...

  sin(2θ) = 2(-8/17)(-15/17) = 240/289

_____

Additional comment

The attached calculator result comes from the principal value of the arcsine function resulting in a 4th-quadrant angle for negative sine values. Double that angle will still be a 4th-quadrant angle. When the translation is made to the appropriate quadrant, the desired double angle will be a 1st-quadrant angle with a positive sine.

If (x + 8) is a factor of f(x), then the true statement is f(-8) = 0 .

In the question ,

it is given that , x \(+\) 8 is factor of f(x) ,

we have to select the correct option about f(x) from the given options .

When solving the polynomials, a factor of the polynomial gives the solution of  the polynomial.

that means , x + 8 = 0

So , x = -8 ,

So , it means that when x = -8 , then the value of the function f(-8) will be zero ,

which means that x = -8 will be a root of the given function f(x) .

Therefore , the true statement is f(-8) = 0 .

The given question is incomplete , the complete question is

If (x + 8) is a factor of f(x), which of the following must be true ?

(a) Both x = –8 and x = 8 are roots of f(x).

(b) Neither x = –8 nor x = 8 is a root of f(x).

(c) f(–8) = 0

(d) f(8) = 0

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Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

Answer: The 95% confidence interval is approximately (55.57, 58.43)

======================================================

Explanation:

At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.

The sample size is n = 17

The sample mean is xbar = 57

The population standard deviation is sigma = 3

The lower bound of the confidence interval is

L = xbar - z*sigma/sqrt(n)

L = 57 - 1.960*3/sqrt(17)

L = 55.5738905247863

L = 55.57

The upper bound is

U = xbar + z*sigma/sqrt(n)

U = 57 + 1.960*3/sqrt(17)

U = 58.4261094752137

U = 58.43

Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

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Answer:  Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.

Step-by-step explanation:

The total surface area of solid is,

S = 220 m²

And,  The volume of the prism is, 200 m³

We have to given that;

A solid prism is shown in figure.

Since, The surface area of a prism is,

S = (2 × Base Area) + (Base perimeter × height)

Where, "S" is the surface area of the prism.

Hence, We get;

base area = 5 x 10 = 50 m²

height = 4 m

Base Perimeter = 2 (5 + 10) = 30

Hence, We get;

S = (2 x 50) + (30 x 4)

S = 100 + 120

S = 220 m²

Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

Now, For given figure,

Volume of the prism = base area × height

base area = 5 x 10 = 50 m²

height = 4 m

Hence, Volume = 50 × 4 m³

= 200 m³

Thus, The volume of the prism is, 200 m³

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If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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Answer:

14/20

Step-by-step explanation:

Notes are commonly issued on discounted value when the issuer needs to raise funds quickly and is willing to accept a lower price for the note in exchange for immediate cash.

Notes can be issued either at their face value or at a discounted value.

A note is issued at its face value, the price of the note is the same as the face value of the note.

This is known as issuing the note at par value or face value.

A note is issued at a discounted value, the price of the note is lower than the face value of the note.

This is known as issuing the note at a discount.

The difference between the face value of the note and the discounted value is called the discount.

The investor who purchases the note at a discounted value will receive the face value of the note when it matures.

Notes may be issued at face value or at a discount from that amount.

The price of a note is equal to its face value when it is issued, or at face value.

The note will then be issued at face value or par value.

A note is sold for less than its face value when it is issued at a reduced price.

This is referred to as discounting the note's issuance.

The discount is the amount that separates the note's face value from its reduced value.

The face value of the note will be paid to the investor who paid the reduced price when the note matures.

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

5:08 PM

Step-by-step explanation:

1:45 plus 1 hour and 13 minutes equals 2:58. 35 minutes added to 2:58 equals 3:33. Finally 3:33 PM added to 1 hour and 35 minutes equals 5:08 PM.

(a) The correct option is (A)

(b) The correct option is (B)

The root of a number n is another number, when multiplied by itself a given number of times, equals n.

(a)

The given term is,

-11+√10

Since, The value of √10 =3.1622

-11+√10  = -11+3.1622

              = -7.8377

              = -7.83(approx)

The answer is -7.83.

(b)

The given term is,

(11-(2/5)×5)² + (1-4)²

=(11-2)²+(-3)²

= 9²+9

= 81+9

= 90

The Answer is 90.

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Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Step-by-step explanation:

we first of all move 20 behind the comma for it to become -20 +3 and we get -17.

then use the product =-34

sum = 3

factors then continue

Answer:

\(x= \frac{-3 - \sqrt{145} }{4} \ \ or\ \ x= \frac{-3 + \sqrt{145} }{4}\)

Step-by-step explanation:

2x² + 3x + 3 = 20​

⇔ 2x² + 3x + 3 - 20 = 0

⇔ 2x² + 3x - 17 = 0

Using the Quadratic Formula to solve a Quadratic Equation :

\(x= \frac{-b \pm \sqrt{b^{2}-4ac} }{2a}\)

In the equation 2x² + 3x - 17 = 0

a = 2  ,  b = 3  and c = -17

Then

b² - 4ac = 3² - 4×2×(-17)

           = 9 + 8 × 17    

           = 9 + 136    

           = 145

Then

b² - 4ac > 0

Then

\(x= \frac{-3 \pm \sqrt{145} }{2 \times 2}\)

Then

\(x= \frac{-3 \pm \sqrt{145} }{4}\)

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer: 8 cows mooed

Step-by-step explanation:

The least common multiple of 598 and 45 is 26, 910

To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.

This gives:

598 prime factorization :

2 x 13 x 23 = 598

45 prime factorization :

3 x 3 x 5 = 45

The least common multiple is;

= 2 x 13 x 23 x 3 x 3 x 5

= 26, 910

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