Sabina and Lou are reading the same book. Sabina reads 12 pages a day. She had read 36 pages when Lou started the book, and Lou reads at a pace of 15 pages per day. If their reading rates continue, will Sabina and Lou ever be reading the same page on the same day? Explain.

Answer:

letter C

Step-by-step explanation:

She substitue the X-Intercept, (3,0), for B

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Answer:

1)

90g strawberry jelly

6 sponge fingers

315ml custard

135g tinned fruit

2) 260 cm²

Step-by-step explanation:

1) 120/4 × 3

90g strawberry jelly

8/4 × 3

6 sponge fingers

420/4 × 3

315ml custard

180/4 × 3

135g tinned fruit

2) area = base × height

= 20 × 13

= 260 cm²

Answers and Step-by-step explanations:

1. Let's find the amount of each ingredient we need for 1 person, and then multiply that by 3 later.

strawberry jelly: we have 120 grams for 4 people, so for 1 person, we need 120/4 = 30 grams

sponge fingers: we have 8 of these for 4 people, so for 1 person, we need 8/4 = 2 sponge fingers

custard: we have 420 mL for 4 people, so for 1 person, we need 420/4 = 105 mL

tinned fruit: we have 180 grams for 4 people, so for 1 person, we need 180/4 = 45 grams

Now, multiply each of these by 3 to find the amount needed for 3 people:

strawberry jelly: 30 grams * 3 = 90 grams

sponge fingers: 2 sponge fingers * 3 = 6 sponge fingers

custard: 105 mL * 3 = 315 mL

tinned fruit: 45 grams * 3 = 135 grams

2. The area of a parallelogram is calculated by the formula: A = Bh, where B is the base length (usually a side length) and h is the height perpendicular to the base. Here, we see that have two potential base lengths: 20 and 15. However, looking at the height, it's only perpendicular to the base with length 20, so we know that B = 20 and h = 13.

Plugging these into the formula, we get: A = 20 * 13 = 260 cm squared.

Hope this helps!

Answer:

5.5%

Step-by-step explanation:

To solve this problem we can use a modified version of the simple interest formula which is shown below:

[tex]r=\frac{I}{Pt}[/tex]

I = interest amount

P = principal amount

t = time (years)

The first step is to find the interest gained from the investment.

[tex]3,123.75-2,450=673.75[/tex]

Next, plug in the values into the equation:

[tex]r=\frac{673.75}{(2,450)(5)}[/tex]     Multiply the bottom values

[tex]r=\frac{673.75}{12,550}[/tex]         Divide the values

[tex]r=.055[/tex]

The last step is to convert 0.055 into a percent:

[tex]0.055(100)=5.5[/tex]

The interest rate is 5.5%

Answer:

all work is shown and pictured

The length of the major arc LNM, in terms of pi, is 29π/6 yards.

The circle has a radius of 3 yards and the central angle m∠LKM is 70°. Since the question asks for the length of the major arc LNM, we first need to calculate the angle of the major arc. The angle of a full circle is 360°, so the angle of the major arc will be 360° - 70° = 290°.

To find the arc length, we use the formula for arc length (l) which is: l = rθ (in radians). We must convert the angle from degrees to radians by multiplying by π/180. So, 290° becomes (290π/180) radians.

Now, compute the length of the major arc LNM: l = 3 yd * (290π/180) = (870π/180) yd, which simplifies to: 29π/6 yd. Thus, the length of the major arc LNM, in terms of π, is 29π/6 yards.

Answer:

44.057 to nearest hundredth

44.06

Answer: 1280

Step-by-step explanation:

The fourth term is 8 times the first term.

The fourth term = [tex]ar^3[/tex]

[tex]ar^{3} = 8a[/tex]

To find the common ratio:

∴ [tex]\frac{ar^3}{a} = \frac{8a}{a}\\[/tex]

∴ [tex]r^3 = 8\\r = 2\\[/tex]

Common ratio = 2

To find the nth number of terms = [tex]\frac{a(r^n -1)}{r-1\\}[/tex]

∴ [tex]\frac{a(2^{10} -1)}{2-1}[/tex]

∴ [tex]1023a\\[/tex]

The sum of 10 terms = 1023a

The sum of 10 terms = 2557.5

∵ 2557.5 = 1023a

∵ [tex]a = \frac{5}{2}[/tex]

To find the 10th term:

∴ [tex]ar^9\\[/tex]

∴ [tex]\frac{5}{2} *2^9[/tex]

⇒ 1280   ║ answer.

From the question given above, we were told that the fourth term is 8 times the first term. This can be written as:

T₄ = 8a

But

T₄ = ar³

a => is the first term

r => is the common ratio

Thus,

ar³ = 8a

Solving for the common ratio (r):

ar³ = 8a

Divide both side by a

r³ = 8

Take the cube root of both side

r = ³√8

r = 2

Thus, the common ratio (r) is 2

Next, we shall determine the first term (a). This can be obtained as follow:

Sum of 10th term (S₁₀) = 2557.5

Common ratio (r) = 2

Number of term (n) = 10

Sₙ = a[rⁿ – 1] / r – 1

2557.5 = a[2¹⁰ – 1] / 2 – 1

2557.5 = a[1024 – 1]

2557.5 = 1023a

Divide both side by 1023

a = 2557.5 / 1023

a = 2.5

Thus, the first term is 2.5

Finally, we shall determine the 10th term of the sequence. This can be obtained as follow:

Common ratio (r) = 2

First term (a) = 2.5

T₁₀ = ar⁹

T₁₀ = 2.5 × 2⁹

T₁₀ = 2.5 × 512

T₁₀ = 1280

Therefore, the 10th term of the sequence is 1280

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Answer:

see the explanation

Step-by-step explanation:

The complete question is

The dimensions of the square pyramid are

Base: 40 inches

Height: 12 inches

step 1

Find the volume of the square pyramid

The volume of the square Pyramid is given by the formula

[tex]V=\frac{1}{3}b^2h[/tex]

where

b is the length side of the square base

h is the height of the pyramid

we have

[tex]b=40\ in\\h=12\ in[/tex]

substitute

[tex]V=\frac{1}{3}(40)^2(12)[/tex]

[tex]V=6,400\ in^3[/tex]

step 2

Find the volume of sand

Multiply the number of bags of sand by the volume of each bag

so

[tex]3(1,200)=3,600\ in^3[/tex]

step 3

Compare the volume of the sand with the volume of the square pyramid

3,600 < 6,400

therefore

Kaytlyn has not enough sand to build the castle

Answer: 3

15(3)-15=30

45-15=30

30=30

15x-15=30

15x=45

x=3

Answer:

Step-by-step explanation:

[tex]\sf 15x-15=30[/tex]

[tex]\sf 15x-15+15=30+15[/tex]

[tex]\sf 15x=45[/tex]

[tex]\sf \frac{15x}{15}=\frac{45}{15}[/tex]

[tex]\sf x=3[/tex]

Answer:

(m+5) (m-9) = 0

Step-by-step explanation:

An equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation.

Given that, the solutions of an equation are m = -5, and m = 9, we need to find the equation,

(m + 5) (m - 9) = 0

One possibility is that of a quadratic equation.

y = (m + 5) (m - 9)

y = m² - 9m + 5m - 45

y = m² - 4m - 45

Hence, an equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.

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Answer:

a) [tex]\sqrt{64+x^2}[/tex]

b) 15

Step-by-step explanation:

a) We know that AB = 8 and BC = x. We can use the Pythagorean Theorem, which states that for a right triangle with sides a, b, and c: [tex]a^2 +b^2=c^2[/tex] , where a and b are the shortest sides and c is the longest.

Here, AB = a = 8 and BC = b = x. So, AC = c. Then:

[tex]AB^2+BC^2=AC^2[/tex]

[tex]8^2+x^2=AC^2[/tex]

[tex]AC=\sqrt{64+x^2}[/tex]

b) We know that AC - AB = 9. Since AB = 8, then AC = 9 + 8 = 17. We also have the expression from above, so set them equal:

[tex]AC=\sqrt{64+x^2}=17[/tex]

[tex]64+x^2=289[/tex]

[tex]x^2=225[/tex]

x = 15

Hope this helps!

Answer:

sqrt(x^2 +64) = AC

x = 15

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 =c^2  a and b are the legs and c is the hypotenuse

We know the legs are x and 8

x^2 + 8^2 = AC^2

x^2 + 64= AC^2

Solving for AC

Take the square root of each side

sqrt(x^2 + 64) = sqrt(AC^2)

sqrt(x^2 +64) = AC

We are given AC - AB = 9

We know AB = 8

AC -8 =9

Add 8 to each side

AC -8+8 = 9+8

AC = 17

AC is the hypotenuse,

x^2 + 64= AC^2

x^2 +64 = 17^2

x^2 +64 = 289

Subtract 64  from each side

x^2 +64-64 = 289-64

x^2 =225

Take the square root

sqrt(x^2) = sqrt(225)

x =15

Answer:

247

Step-by-step explanation:

Hello!

We can begin by finding the average and median before two numbers are removed.

(9 + 13 + 15 + 17 + 19 + 23 + 31 + 49) / 8  = 22

And the median!

(17 + 19)/ 2  =  18

Since we know that the average and median will increase by 2, we will have the median after removal as 20, and the average, 24.

For the average, we can see that the total must be 144, that's what 24 * 6 is.

19 must have been one of the numbers because (17 + 23) / 2  = 20.

That's 32 less than the original sum of 176.

So if one of the removed numbers is 19, the other must be 13.

13 * 19 = 247

Thus, the product of the removed numbers are [tex]\boxed{247}[/tex].

Hope this helps!

Answer:

i think, it is option c.

Answer:

n/5 +12

Step-by-step explanation:

Answer:

3:20 pm.

Step-by-step explanation:

Time Yasmin got home: 4:25

Time it took to walk home: 15 minutes

Practice started: 20 minutes after bell.

Practice lasted for 30 minutes.

For us to find this out, you have to calculate all the activities.

An hour is 60 minutes.

A half hour is 30 minutes.

15 + 20 + 30 = 65 minutes.

65 minutes = an hour and five minutes.

4:25 - 1:05 = 3:20.

Feel free to let me know if you need more help! :)

Answer:

3:20 p.m

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Hi there,

To find the least common multiple (LCM) of 2 numbers, I would recommend listing off a few multiples of each number. Since they are small, it shouldn't be too hard.

Multiples of 4:

4, 8, 12, 16, 20

Multiples of 5:

5, 10, 15, 20

As you can see, the first multiple that 4 and 5 both share is 20. So the least common multiple of 4 and 5 20.

Final answer:

Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.

Explanation:

Given:

Lengths of the larger prism: 4 feet, 3 feet, 4 feet

Dimensions of the stacked prisms: 4 feet, 3 feet, 2 feet

Let: The lengths, widths, and heights of the smaller prism be L, W, and H respectively.

Two proportions:

4/L = 4/3

3/W = 3/2

Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.

Step-by-step explanation:

a. 6 * (-3) = - 18

b. (-5) * 4 = - 20

c. (-9) * (-2) = 18

Answer:

Total length of the rectangle = 14+14= 28cm

width= 7 cm

Area of the rectangle = 28×7cm²

= 196 cm²

Area of 2 semicircles = Area of 1 circle

= π(7)² = 3.14×49= 153.86cm²

Area of the shaded region = 196-153.86

= 42.14 cm²

Answer: 42.14 [tex]cm^2[/tex]

Step-by-step explanation:

Assuming that the width of the rectangle is 7 cm, the semi-circle's radius is also 7 cm.

Let's calculate the area of the two semi-circles, which in total makes a whole circle.

The formula for a circle is [tex]a=2\pi r^2[/tex]

Since r = 7, plug it in the formula:

[tex]a=2\pi (7)^2[/tex]

[tex]a=49\pi =153.86 cm^2[/tex]

Now, to figure out the length of the rectangle, look at the semi-circles. Their radius is 7 cm, so their diameter is 14 cm. We have two semi-circles with the diameter (14 cm), so we can say that the width is 28 cm.

Area of a rectangle: [tex]a=lw[/tex]

[tex]a=7*28=196cm^2[/tex]

To find the area of the shaded region, we subtract the area of the semi-circles to the rectangle, which should be:

[tex]196 - 153.86=42.14 cm^2[/tex]

Answer:

45ft

Step-by-step explanation:

The remaining piece has to be found. How far away is the end of the pole from the base of the pole along the ground.

We deduct original to broken 81-28 = 53 feet tall.  

PT + to find the other side.

53^2 - 28^2 = S^2

√2025 = 45 = S^2

S^2 = 45ft

Answer:

6 laps

Step-by-step explanation:

Jeffery needs to run 3 laps.

To find the number of laps that Jeffery needs to run, we can set up a proportion. We know that 1 lap is equal to 1 tenth of a mile, so we can set up the following proportion:

1 lap / 1 tenth mile = x laps / 3 fifths mile

Cross-multiplying and solving for x, we get:

x = (1 lap * 3 fifths mile) / (1 tenth mile)

x = 3 laps / 1 lap

x = 3

Therefore, Jeffery needs to run 3 laps.

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Answer:

70 degrees

Step-by-step explanation:

The adjacent angles in a parallelogram are supplementary and add to 180 degrees

∠CDE+∠DEF=180

We know that ∠CDE is 110 degrees, so we can substitute that in

∠CDE+∠DEF=180

110+∠DEF=180

Subtract 110 from both sides

∠DEF= 70

So, ∠E is 70 degrees

Answer:  24

Step-by-step explanation:  The first few multiples of 8 are: 8, 16, 24, 32, 40, and 48. The first multiples of 12 are: 12, 24, 36, 48, 60, and 72.

...

Step 1: List the Multiples of Each Number.

Answer:

3 : 6 : 1

Step-by-step explanation:

The common multiple between these numbers is 9, so divide everything by nine.

Answer:

3:6:1

Step-by-step explanation:

27/9=3

54/9=6

9/9=1

3:6:1

I hope this helps!

Answer:

2401

Step-by-step explanation:

7 * 7 * 7 * 7 = 2401

Answer:

the answer is b.

Step-by-step explanation:

Answer:

36 feet squared

Step-by-step explanation:

Finding the perimeter of an object is adding all of the sides together. If the width of the rug is 6 feet then we know that there are two sides that length. Add those together.

6 feet + 6 feet = 12 feet

You would subtract the number you get from the perimeter.

24 feet - 12 feet = 12 feet

And then divide the number by the number of sides left, 2, to get each of their lengths.

12 feet / 2 feet = 6 feet

To find the area of a rectangle you multiply length times width, which in this case both are 6 feets.

6 feet x 6 feet = 36 feet squared

Answer:

Step-by-step explanation:

Solution:-

- We will denote:

          Number of Lions = x

          Number of bears = y

          Number of elephants = z

          Any other animal = T

- Now we will mathematically each statement given by the trainer.

Statement 1:

"7 times as many lions than other animals (not lions)."

- There were 7 times as many lions than any other animals i.e ( bears and elephants). So we can express:

                       x = 7*( x + y + T)   .... E 1

Statement 2:

"there were a seventh as many bears as other animals"

- There were 1/7 as many bears than any other animals i.e ( lions and elephants). So we can express:

                       y = (x+z+T) / 7  ... E2

- Now combine two decrypted mathematical expressions.

                       x + y + z = T

                       7T + T/7 + z = T

Transformation involves changing the position of a shape

The coordinates of Y' are (-5, 5)

The vertices are given as:

X(2, 4), Y(-3, 4), and Z(-3,1)

The transformation rule is given as:

(x, y) → (x - 2, y + 1)

For vertex Y, we have:

(-3, 4) → (-3 - 2, 4 + 1)

Simplify

(-3, 4) → (-5, 5)

Hence, the coordinates of Y' are (-5, 5)

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