CHECKING YOUR UNDERSTANDING
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper
1. A dinner plate has a diameter of 10.2 cm. What is the area of the dinner plate?
A. 81.67 cm
C. 93.84 cm
B. 85.12 cm
D. 100.02 cm
2. A dog is tied to a wooden stake in a yard. His leash is 3 m long, and he runs around
in circles pulling the leash as far as it can go. How much area does the dog have
to run around ?
A. 26.28 m2
C. 29.66 m2
B. 28.26 m2
D. 32.28 m²
3. A storm is expected to hit 7 mi in every direction from a small town of Malabon.
What is the area that the storm will affect?
A. 116.68 mi
C. 150.67 mi
B. 124.83 mi
D. 153.86 mi
4. Every December, an amusement park is constructed in Malabon Robinsons Town
mall. A carousel is the most favorite ride of the kids there. The diameter of the
carousel is 20.5 m. What is the area of the carousel?
A. 329.90 m²
C. 392.90 m2
B. 328.90 m2
D. 391.90 m2
5. A lawn sprinkler sprays water 4.5 ft in every direction as it rotates. What is the area
of the sprinkled lawn?
A. 56.885 ft
C. 63.585 ft
B. 60.855 ft
D. 65.385 ft ​

Given:

The given sum is:

[tex]\sum _{k=4}^9(5k+3)[/tex]

To find:

The expanded form and find the sum.

Solution:

We have,

[tex]\sum _{k=4}^9(5k+3)[/tex]

The expanded form of given sum is:

[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]

[tex]\sum _{k=4}^9(5k+3)=213[/tex]

Therefore, the correct option is C.

Answer:

4/5 of a fruit bar

Step-by-step explanation:

Answer:

[tex]6.7159[/tex]

Step-by-step explanation:

[tex]\mu=48.8\\n=35\\\bar{x}=53.8\\\sigma=4.4\\\alpha=1\%=0.01[/tex]

Null and alternative hypothesis :

[tex]H_0:\mu=48.8\\H_a:\mu>48.8[/tex]

Test statistic,

[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]\Rightarrow t=\frac{53.8-48.8}{\frac{4.4}{\sqrt{35}}}[/tex]

[tex]\Rightarrow t=\frac{5\times 5.91}{4.4}[/tex]

[tex]\Rightarrow t=6.715[/tex]

Test statistic [tex]t=6.715[/tex]

[tex]P-[/tex]value [tex]=P(t>6.715)[/tex]

[tex]P-[/tex] value [tex]=0.0001[/tex]  by the p- table

Significance level [tex]0.01[/tex]

         [tex]p-[/tex]value [tex]<0.01[/tex]

  We reject [tex]H_0[/tex]

Answer: 14 units

Step-by-step explanation:

Answer:

for the solve and check:

[tex]2\frac{3}{8}+x=3\frac{1}{4} \\2\frac{3}{8}-2\frac{3}{8}+x=3\frac{1}{4}-2\frac{3}{8}\\\\x=3\frac{1}{4}-2\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]

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

[tex]3\frac{3}{8}+x=4\frac{1}{4} \\3\frac{3}{8}-3\frac{3}{8}+x=4\frac{1}{4}-3\frac{3}{8}\\\\x=4\frac{1}{4}-3\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]

for the second solve and check:

[tex]4\frac{3}{8}+x=5\frac{1}{4} \\4\frac{3}{8}-4\frac{3}{8}+x=5\frac{1}{4}-4\frac{3}{8}\\\\x=5\frac{1}{4}-4\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]

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

[tex]5\frac{3}{8}+x=6\frac{1}{4} \\5\frac{3}{8}-5\frac{3}{8}+x=6\frac{1}{4}-5\frac{3}{8}\\\\x=6\frac{1}{4}-5\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]

Answer:

Step-by-step explanation:

Green picture

x = 2.25 ft = 2 1/4 ft

we substitute 2 1/4 for x

x = 2 1/4 ft

3 3/4 ft + 2 1/4 ft  = 6 ft

6 ft = 6 ft

Since 6ft is equal to 6ft...

Blue picture

It is 2 1/4 ft long

we substitute 7/8 ft for x

since 2 1/4 ft is equal ...

Yellow picture

2 3/8 ft - 2 3/8 ft + x = 3 1/4 ft - 2 3/8 ft

x = 3 1/4 ft - 2 3/8 ft

x = 7/8 ft

Check

x = 7/8 ft

2 3/8 ft + 7/8 ft = 3 1/4 ft

3 3/8 ft - 3 3/8 ft + x = 4 1/4 ft - 3 3/8 ft

x= 4 1/4 ft - 3 3/8 ft

x = 7/8 ft

check

x = 7/8 ft

3 3/8 ft + 7/8 ft = 4 1/4 ft

red picture

4 3/8 ft - 4 3/8 ft + x = 5 1/4 ft - 4 3/8 ft

x = 5 1/4 ft - 4 3/8 ft

x = 7/8 ft

check

x = 7/8 ft

4 3/8 ft + 7/8 ft = 5 1/4 ft

Answer:

≈ 0.52

Step-by-step explanation:

P( head ) = 2/3 , P( tail ) = 1/3

when a head is tossed ; Gambler A wins $1

when a tail is tossed : Gambler B wins $1

Determine the P( Gambler A wins the game ) if he starts with I dollars

Assuming I = $1

n = 5

p ( head ) = P( winning ) = 0.66

p( losing ) = 0.33

applying the conditional probability in Markov which is ;

Pₓ = pPₓ₊₁ + (1 - p) Pₓ₋₁

P( 1) = 0.66P₂ + 0.33P₀

resolving the above using with Markov probability

P( 1 ) = 0.51613

hence the probability of Gambler A winning the game if he starts with $1

≈ 0.52

Answer:

13 minutes

Step-by-step explanation:

The reason why it is 13 minutes is because you subtract 10:41 AM from 10:28 AM and you get 13 minutes.

Answer:

13

Step-by-step explanation:

41-28= 13

the hours don't change so you just need to subtract the minutes

Answer:

4

Hope that this helps!

Answer:

The nth term is 27 - 30(n-1) or can be simplified to 57 - 30n.

Step-by-step explanation:

This is an arithmetic sequence (ie. each term equals the previous term with a constant value added (or subtracted from it)

T1 = 27

T2 = -3 = T1 - 30 = 27 - 30

T3 = -33 = T2 -30 = 27 -30 - 30=27-30X(2)

T4= -63 = T3 - 30 =27-30X(2)-30=27-30X(3)

In general, the nth term of this sequence:

S(n) = 27 - 30X(n-1)

Answer:

[tex]P(Work | Senior) = 0.14[/tex]

Step-by-step explanation:

Given

The attached table

Required

[tex]P(Work | Senior)[/tex]

This is calculated using:

[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]

This gives:

[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]

From the table:

[tex]n(Work \ n\ Senior) = 5[/tex]

[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]

So:

[tex]P(Work | Senior) = \frac{5}{35}[/tex]

[tex]P(Work | Senior) = 0.14[/tex]

Answer:

14%

Step-by-step explanation:

add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

Answer:

90°

Step-by-step explanation:

It's simple, the angle of a line is 180°

∠EFG=90°

Line GD-∠EFG=180°-90°=90°

Please mark brainliest!

Answer:

Step-by-step explanation:

1/48 + 5/6    

The LCD of 48 and 6 is 48 so we have:

1/48 + 40/48

= 41/38

Answer:

41/48

Step-by-step explanation:

Answer:

value for X

3x-4 =41

3x =41+4

3x =45

x =15

Answer:

The father is 42 years old and the son is 12 years old.

Step-by-step explanation:

Since three years ago the sum of the ages of father and his son was 48 years, and three years hence father's age will be three times that of his are his, to find the present ages of the father and his are his, the following calculations must be performed:

F + S = 48

F + 6 + S + 6 = 3S

34 + 14 = 48 /// 34 + 6 = 40 --- 14 + 6 = 20 (x 3 = 60)

38 + 10 = 48 /// 38 + 6 = 44 --- 10 + 6 = 16 (x 3 = 48)

40 + 8 = 48 /// 40 + 6 = 46 --- 8 + 6 = 14 (x 3 = 42)

39 + 9 = 48 /// 39 + 6 = 45 --- 9 + 6 = 15 (x 3 = 45)

39 + 3 = 42

9 + 3 = 12

Therefore, the father is 42 years old and the son is 12 years old.

Answer:

El polinomio final es:

[tex]=x(\frac{1}{3}y^{2}-3+\frac{2}{3}xy)[/tex]

Step-by-step explanation:

Agrupemos los términos con las mismas variables:

[tex](\frac{2}{3}xy^{2}-\frac{1}{3}xy^{2})+(2x-5x)+\frac{2}{3}x^{2}y=[/tex]

Sumemos estos terminos:

[tex]=\frac{1}{3}xy^{2}-3x+\frac{2}{3}x^{2}y=[/tex]

Podemos ver que los tres terminos tienen x, asi que podemos factorizar x.

Por lo tanto el polinomio final es:

[tex]=x(\frac{1}{3}y^{2}-3+\frac{2}{3}xy)[/tex]

Espero te haya servido.

El resultado de simplificar  [tex]\frac{2}{3}xy^2+2x-\frac{1}{3}xy^2+\frac{2}{3}x^2y-5x[/tex] es

[tex](\frac{1}{3}y^2+\frac{2}{3}xy-3)x[/tex]

El polinomio que queremos simplificar es

[tex]\frac{2}{3}xy^2+2x-\frac{1}{3}xy^2+\frac{2}{3}x^2y-5x[/tex]

primero, recopilamos términos similares

[tex]\frac{2}{3}xy^2-\frac{1}{3}xy^2+\frac{2}{3}x^2y+2x-5x[/tex]

luego simplificamos los términos similares. Es decir

Para el [tex]xy^2[/tex] términos:

[tex]\frac{2}{3}xy^2-\frac{1}{3}xy^2=(\frac{2}{3}-\frac{1}{3})xy^2\\\\=(\frac{1}{3})xy^2=\frac{1}{3}xy^2[/tex]

y para el [tex]x[/tex] términos:

[tex]2x-5x=(2-5)x\\=(-3)x=-3x[/tex]

la [tex]x^2y[/tex] términos ya está simplificado. Así que déjalo así.

Este es el trabajo total:

[tex]\frac{2}{3}xy^2-\frac{1}{3}xy^2+\frac{2}{3}x^2y+2x-5x\\\\=(\frac{2}{3}-\frac{1}{3})xy^2+\frac{2}{3}x^2y+(2-5)x\\\\=(\frac{1}{3})xy^2+\frac{2}{3}x^2y+(-3)x\\\\=\frac{1}{3}xy^2+\frac{2}{3}x^2y-3x[/tex]

Incluso podemos factorizar la respuesta final para obtener

[tex](\frac{1}{3}y^2+\frac{2}{3}xy-3)x[/tex]

Obtenga más información sobre la simplificación aquí: https://brainly.com/question/25014973

Answer:

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Answer:Center =(-5,-7)

Step-by-step explanation:

Step-by-step explanation:

for mixed number to a improper fraction you take the whole number and times that by the denominator and add the numeriator

for example

[tex]8 \frac{3}{8} [/tex]

8 x 8 = 64

64 + 3 = 67

and after you get your last number (67) you put that over your original denominator which is 8 so it would be

[tex] \frac{67}{8} [/tex]

for the improper to mixed you see how many times you denominator goes into your numerator

another example is

[tex] \frac{13}{7} [/tex]

7 goes into 13 twice so your whole number is 2 and you have a remaining 1 so it would look like

[tex]2 \frac{1}{7} [/tex]

Answer:

A) 9/4

B) 67/8

C) 17/6

D) 9/2

E) 16/3

F) 127/12

G) 37/4

H) 41/6

Q) Whole Number: 1 Fraction: 6/7

R) Whole Number: 4 Fraction: 1/2

S) Whole Number: 1 Fraction: 8/9

T) Whole Number: 2 Fraction: 1/3

U) Whole Number: 2 Fraction: 3/7

V) Whole Number: 3 Fraction: 1/3

W) I am not 100% sure for this one but I think it's right.

Mixed Number - Whole Number: 1 Fraction: 5/8

Improper fraction - 13/8

Step-by-step explanation:

With improper fractions the first thing that you want to do is multiply the whole number with the denominator (the number on the bottom of the fraction), then add the numerator (the number on the top of the fraction). You also want to keep the denominator the same in both fractions.

When working with converting mixed fractions into improper fractions it is kind of the opposite, but it is a little harder to explain. Let's take letter Q as an example. If you know that you cannot divide the numerator and the denominator in anyway to make a whole number, the whole number will become a one and the numerator is how many are left. so in this case the answer for Q would be 1 6/7, 1 being the whole number and 6 from 6+7=13. now let's look at letter R, you know you can divide 2 four times into 9, the whole number will be 4 and the fraction will be 1/2, 4x2+1=9. You can also double check that you did it right by turning it back into a improper fraction from the mixed number state by multiplying the denominator with the whole number, then adding the numerator. Hope that made sense, send me a DM if you need more help!

Answer:

2, 3, 4 (up to down)

Step-by-step explanation:

Rational: can be terminating, repeating, in a fraction

Irrational: Not terminating (ending), doesn't repeat (o.33333....), and you can't put it in a fraction

Hope this helps!!

p.s. brainliest plz

Answer:

its not loading

Step-by-step explanation:

Step-by-step explanation:

Thanks, so cube root of 512 is 8 and reciprocal of 0.4 is 2.5 then:

8 : 2.5 / divide both by 2.5 to get:

3.2 : 1 that's my answer right?

The correct form of the ratio of cube root of 512: reciprocal of 0.4 is 3.2:1

It is a number y such that y to the power 3 is equal to x.

We have to find the ratio of cube root of 512 and the reciprocal of 0.4  which will be as follows

cube root of 512:  reciprocal of 0.4

8: 1/0.4

8=2.5

dividing by 2.5

3.2 : 1

Hence the ratio will be 3.2 :1 of cube root of 512 and the reciprocal of 0.4

Learn more about cube root at https://brainly.com/question/310302

#SPJ2

Answer:

7776pi cubic inches

Step-by-step explanation:

Answer:

D1 to D3: SF = 3 / 2. Equation = 9 / 6 = 3 / 2

D2 to D3: SF = 2. Equation = 9 / 4.5 = 18 / 9 = 2

D3 to D1: SF = 2 / 3. Equation = 6 / 9 = 2 / 3

Step-by-step explanation:

Let me just make sure.

Answer:

Step-by-step explanation:

Answer:

98?

Step-by-step explanation: