Now Ann is x years old and her sister is eight years younger than her. After five years , Anne's age is twice the age of her sister.

Write down the ages of Anne and her sister after five years in terms of x.

Please help me friends

The given example is inductive reasoning.

The method of arriving at a conclusion based on a series of observations is known as inductive reasoning. It is not a valid method of proof in and of itself.

We have the information that. Janelle got invited to a shopping spree with a friend and is supposed to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,

she has noticed that it takes about two hours for her to travel to the mall. she has also noticed that it takes her 30 minutes to get ready before leaving her apartment. she concludes that she needs to start getting ready at 0:30 p.m.

The given information is giving us the series of the data like we are having a sequence of the timing at what time what she did so we have a series of observations here.

Therefore the given example is inductive reasoning.

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Answer:

47.5 games

Step-by-step explanation:

Finding A :

⇒ Games by A : Games by B = 3 : 1

⇒ Games by A : 10 = 3 : 1

⇒ Games by A = 30

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

Finding C :

⇒ Games by B / Games by C × Games by A / Games by B = 3 × 4/3

⇒ Games by A / Games by C = 4

⇒ Games by C = 30/4

⇒ Games by C = 7.5

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

Total games won :

⇒ Games by A + Games by B + Games by C

⇒ 30 + 10 + 7.5

⇒ 47.5 games

The solution of the given radical expression√20 using factorization is [tex]2 \sqrt{5}[/tex]. Therefore, the correct option for the  radical expression√20 is option A, i.e  [tex]2 \sqrt{5}[/tex].

A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression.

Example = 4y, 3x+4.

An expression containing the values in the form of square root, cube root is called a radical expression.

The breaking of a number into its own factors, so that they multiply to give the same number again, is called factorization.

Given expression, √20

The solution of the expression can be obtained by the factors of 20.

[tex]\sqrt{20} = \sqrt{2\times2\times5}[/tex]

[tex]\sqrt{20}[/tex] = [tex]2 \sqrt{5}[/tex]

Here, 2 and 5 are factors of 20.

Thus, the value of the radical expression [tex]\sqrt{20}[/tex]  is [tex]2 \sqrt{5}[/tex].

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Answer:

Step-by-step explanation:

Answer:

By using the pythsgorean theorem! simple

Answer:[tex]\sqrt{155}[/tex]

Step-by-step explanation:

Oh god pythagorean triples got thrown out the window for this one. This will be a bit ugly.

First, we find the other side length of the rectangle using the pythagorean theorem.

Then, we use that side length in ANOTHER pythagorean theorem to get our answer.

Well, we know that the side length is [tex]\sqrt{5^{2}+9^{2} }[/tex]

We'll use whatever that number is, let's call it x for now, in our other expression:

[tex]\sqrt{x^{2}+7^{2}}[/tex]

So we can do this in one clean equation by substituting our first equation as x in the second one.

Or do them separately. Your choice.

Anyways, try to solve this one now that you know what to do. If you need more help then message.

Answer: [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

   We will subtract the amount of water that leaked out from the amount of water originally in the fish tank.

[tex]\displaystyle \frac{3}{4} - \frac{1}{3} =\frac{3*3}{4*3} -\frac{1*4}{3*4} =\frac{9}{12} -\frac{4}{12}=\frac{5}{12}[/tex]

         The fish tank is [tex]\frac{5}{12}[/tex] of the way full.

From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.

A quadratic graph is in form of a parabola opened upward or downward.

According to the question, we are to select a graph that has a coordinate (2, 4) on its curve.

To determine thus, we will locate the value of 2 on the x-axis and value of 4 on the y-intercept and trace whether the intersecting point is on the curve.

From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.

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Answer:

The exponent form of 5670 is 5.67 × 103.

Step-by-step explanation:

you can also use this

it's pretty easy

https://calculator.name/decimal-to-scientific-notation/5670

Answer:

It would be about 1/4

Step-by-step explanation:

The probability that a randomly selected pigeon gets an incorrect result is; 0.0103

We are told that;

1.5% pigeons are infected.

Inaccuracy of the test = 1 - 97% = 3%

1.5% of the pigeons are infected. Thus;

1 - 1.5% = 98.5% pigeons are un-infected.

Inaccuracy of test is 1 - 99% = 1% .

Thus;

0.03 and 0.01 are the probability of an error being made in infected and un-infected respectively.

Meanwhile, probability of infected and un-infected are 0.015 and 0.985 respectively.

Thus, the probability of a randomly chosen person gets an incorrect result = (0.03*0.015) + (0.985*0.01) =  0.0103

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The function in this graph is constant in the range of -4 ≤x≤-2 , Option B is the correct answer.

A function is a mathematical statement which identifies relation between independent and dependent variable.

A graph is given

The graph will be considered constant when the y value is constant for any value of x

The value of y is constant in the range of

-4 ≤x≤-2

Therefore Option B is the correct answer.

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Answer:

It is isosceles by the base angles theorem. It states that when the base angles are equal, the triangle is isosceles.

Step-by-step explanation:

unknown measure : 50°

The original price of the car before 4 years will be $23,032.

Consider the function:

y = P (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, P = original amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

A Naomi's car exponentially depreciates at a rate of 8% per year.

If Nina bought the car when it was 4 years old for $16,500.

Then the original price will be

16500 = P(0.92)⁴

16500 = 0.716P

       P = $ 23,032

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sin A = 4/12 = 1/3

sin inv 1/3 = 19.47⁰

Answer:

option 4, 19.47°

Step-by-step explanation:

From angle A, the given side length are opposite and hypotenuse

SOH CAH TOA is

sinx = opposite / hypotenuse

cosx = adjacent / hypotenuse

tanx = opposite / adjacent

visual representation below

the given length fits the characteristic to use sin

sinA = opposite / hypotenuse

sinA = 4 / 12

common facto is 4 it becomes sinA = 1 / 3

Apply trig inverse property,

x = arcsin(1/3)

x = 19.47122°

Answer:

281x

Step-by-step explanation:

each hat (x) cost 281. x times cost is total

Answer:

864

Step-by-step explanation:

First, you multiply 2 and 6, so it's 12, and multiply it by 144, so it's 1728, and divide it by 2. Therefore, it's 864!

Answer:

$986.28

Step-by-step explanation:

$124.21 + $211.94 = $336.15

700 - 336.15 = 363.85

622.43 + 363.85 = 986.28

34

Step-by-step explanation:

=5x-4y+2z

=5×8-4×3+2×3

=40-12+6

=46-12

=34

Step-by-step explanation:

73° starting temperature.

every hour -2° for 4 hours.

that means -2×4 = -8° during 4 hours.

so, the resulting temperature is

73 - 8 = 65°

Answer:

Step-by-step explanation:

The least amount of money that should be budgeted to paint the monument is $1692.

First step

Using Pythagorean theorem to find the surface area

Since POR is a right triangle

Hence:

PO=20

BR=12

OR=12

PR=√20²+12²

PR=400+144

PR=544

Area of PBC=1/2×24×√544

Area of PBC=12√544

Lateral surface area=4×12√544

Lateral surface area=48√544

Lateral surface area=1119.54²ft

Second step

Since regular paint is  2 coats 200 sq. ft per gallon

Hence:

Number of gallons=1119.54×2/200

Number of gallons= 11.2 gallons

11.2×35= 392

1119.54/80=13 gallons

13×100 =1300

Last step

Least amount=392+1300

Least amount= $1692

Therefore the least amount of money that should be budgeted to paint the monument is $1692.

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Answer:

62.8ft

Step-by-step explanation:

20/2=10 so 10*2=20 so 20*3.14=62.8

62.8

Answer:

314

Step-by-step explanation:

20/2 = 10

10 * 10 = 100

3.14 * 100 = 314

Answer:

[tex]\dfrac{\sqrt[12]{55296} }{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}[/tex]

Multiply the numerator and denominator by [tex]2^{\frac{2}{3}}[/tex] :

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}[/tex]

[tex]\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}[/tex]

Rewrite 1/4 as 3/12 and 2/3 as 8/12 :

[tex]\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:[/tex]

[tex]\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}[/tex]

Simplify the operation in the parentheses:

[tex]\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}[/tex]

[tex]\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}[/tex]

It will take approximately 5.5 years for the investment to be worth $23,000

From the question, we are to determine when the investments will worth $23,000

Using the compound interest formula,

[tex]A = P (1+\frac{r}{n})^{nt}[/tex]

Where A is the amount

P is the principal

r is rate

n is the number of times it is compounded

and t is the time in years

From the given information,

A = $23000

P =$18000

r = 6.7%

n = 4

t = ?

Putting the parameters into the formula, we get

[tex]23000 = 18000(1+\frac{6.7}{100 \times 4})^{4t}[/tex]

[tex]\frac{23000}{18000} = (1.01675)^{4t}[/tex]

[tex]1.4375= (1.01675)^{4t}[/tex]

[tex]1.4375 = (1.0687)^{t}[/tex]

t = 5.46

t ≅ 5.5 years

Hence, it will take approximately 5.5 years for the investment to be worth $23,000

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Answer:

(5, 6)

Step-by-step explanation:

The original coordinate is (1, 1) (3, 1) (1, 4)

Translate four squares : (5, 1) (7, 1) (5, 4)

Translate two squares up: (5, 3) (7, 3) (5, 6)

The vertices of the image is (5, 6)

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]

The given parameters are:

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

[tex]\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1[/tex]

So, we have:

[tex]\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1[/tex]

Evaluate

[tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]

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Answer:

X= 82⁰

z= 82⁰

Step-by-step explanation:

for X:

we can use co-interior angles sum up to make 180 so,

x+ 98= 180

x= 180-90= 82⁰

for z, we can use either angles on a straight line or corresponding angles

98 + z= 180

z= 180-98= 82⁰

corresponding angles are always equal and can be found in the F shape diagram when lines are parallel

therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰

The distance travelled by boat after 1 hour will be 10km.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

The distance will be calculated as:-

a²+b²=c²

9² + 3 ²=  c ²

81+9 = c²

100 = c²

c = 10 km / hour

The distance travelled after one hour will be calculated as:-

Distance = Speed x Time

Distance = 10 x 1 = 10 Km

Therefore the distance travelled by boat after 1 hour will be 10km.

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

As we know, all sides of a Rhombus are equal to each other ~ so we can conclude that :

[tex]\qquad \sf  \dashrightarrow \:4x - 16 = 2x + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x - 2x = 6 + 16[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 22[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 22 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 11[/tex]

Now, plug in the value of x in any equation to get the side length of rhombus ~

[tex]\qquad \sf  \dashrightarrow \:2x + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(11) + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:22 + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:28 \: \: units[/tex]

Side PS = Side QR = 28 units

Answer:

[tex]0.0166[/tex]

Step-by-step explanation:

Let the sample proportion be [tex]\hat{p}=0.14[/tex] and the sample size be [tex]n=439[/tex]:

[tex]\displaystyle \text{Margin of Error}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\text{Margin of Error}=\sqrt{\frac{0.14(1-0.14)}{439}}\\\\\text{Margin of Error}=\pm0.0166[/tex]