A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?

Answer:

9

Step-by-step explanation:

First, find x. Since x is the average of the three number, add the three up and then divided by three. Thus:

[tex]x=\frac{13+-16+6}{3}=3/3=1[/tex]

y is the cube root of 8. Thus:

[tex]y=\sqrt[3]{8}=2[/tex]

So:

[tex]x^2+y^3\\=(1)^2+(2)^3\\=1+8=9[/tex]

Answer:

ljih

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

just do the lcm of denomination and after that start solving

9514 1404 393

Answer:

  1 23/24

Step-by-step explanation:

Fractions can be added when they have the same denominator. Then the addition is performed by adding the numerators, and expressing the sum over the common denominator.

Here, your fractions have denominators of 8 and 6. Usually, we want to find a "least common denominator" to use to express the fractions. There are various ways to find that value. One of the easiest is to consult your memory of multiplication tables to find the smallest number that both a multiple of 8 and a multiple of 6. That number is 24.

An equivalent fraction is one that has the same value, but a different denominator than the one it is being compared to. Equivalent fractions can be made by multiplying by "1" in the form of "a/a" where "a" is any non-zero value. Here, it is useful to multiply 9/8 by 3/3 to make the equivalent fraction 27/24, which has a denominator of 24.

Similarly, we can multiply 5/6 by 4/4 to get the equivalent 20/24, which also has a denominator of 24.

These two fractions can now be added:

  [tex]\dfrac{9}{8}+\dfrac{5}{6}=\dfrac{27}{24}+\dfrac{20}{24}=\dfrac{27+20}{24}=\dfrac{47}{24}[/tex]

If you want to turn this into a "mixed number", you need to find how many times 24 goes into 47: 47÷24 = 1 remainder 23. The quotient is the integer part of the mixed number; the remainder is the numerator of the fractional part. Then the mixed number value of the sum is ...

  [tex]\dfrac{47}{24}=1\dfrac{23}{24}[/tex]

_____

Additional comments

The product of the denominators can always serve as a common denominator. That may not be the "least" common denominator. If you use that here, you would have ...

  [tex]\dfrac{9}{8}+\dfrac{5}{6}=\left(\dfrac{9}{8}\cdot\dfrac{6}{6}\right)+\left(\dfrac{5}{6}\cdot\dfrac{8}{8}\right)=\dfrac{54+40}{48}=\dfrac{94}{48}[/tex]

This result can be reduced by removing a factor of 2 from numerator and denominator to give 47/24, the sum we had above.

The "least common denominator" (LCD) is the Least Common Multiple (LCM) of the denominators. It can be found by forming the product of the unique factors of the denominators. Here, we have 8 = 2·2·2 and 6 = 2·3. The LCD is the product 2·2·2·3. We recognize that 2³ and 3 are unique factors that need to contribute to the LCD. 2 is subsumed by 2³.

As you can see from the factoring, 2 is a common factor of both numbers. Another way to find the LCD (or LCM of the denominators) is to form their product (8×6 = 48) and divide that by the greatest common factor (GCF), which is 2. (48/2 = 24, the LCD) Sometimes it is easier to find the GCF and compute (product/GCF) than to find the LCM using factoring.

__

If you don't mind the possibility of having to reduce the resulting fraction, the sum of fractions can always be computed as ...

  [tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]

This formula computes 94/48 as the sum of these fractions, effectively leaving out the middle step (9/8×6/6 +...) shown in the work above. I find this especially useful for adding rational expressions, not just numerical fractions.

Answer: The length is 4 centimeters and the width is 6 centimeters.

Step-by-step explanation:

If the length of the  rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 .   And we know that to find the area of a rectangle we multiply the length by the width  and they've already given the area  so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2[tex]w^{2}[/tex] - 8w = 24     subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2[tex]w^{2}[/tex] - 8w -24 = 0      divide each term by 2.

[tex]w^{2}[/tex] - 4w - 12 = 0          Five two numbers that multiply to get -12 and to -4

[tex]w^{2}[/tex] +2w - 6w - 12 = 0    Group the left hand side and factor.

w(w+2) -6( w + 2) = 0   factor out w+2

(w+2)(w-6) = 0         Set them both equal zero.

w + 2 =0      or w - 6 = 0  

    -2  -2                + 6   +6

w= -2       or   w=6  

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.  

Now it says that the length is 8 less that twice the width.

So  2(6) - 8 = 12 -8 = 4  So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

Answer:

First convert them which will be

-7/5 - (-4/5)

so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2

so its simply 7/5-4/5 then add a negative sign

so

3/5

now add negative sign so

-3/5

Answer:

what's the problem!?......

angle CDT is the opposite angle of ADN

and the segment DF=FN, so AD= AN

and thats why angle FAN= angle FAD

here, Angle FAN =60,

therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree

and the opposite of ADN is CDT, and the opposite angles are equal.

Hope u got it.

Step-by-step explanation:

hope it helps you.......

[tex]\\ \sf\longmapsto 699^2[/tex]

[tex]\\ \sf\longmapsto (700-1)^2[/tex]

[tex]\\ \sf\longmapsto 700^2-2(700(1)+(1)^2[/tex]

[tex]\\ \sf\longmapsto 490000-1400+1[/tex]

[tex]\\ \sf\longmapsto 488600+1[/tex]

[tex]\\ \sf\longmapsto 488601[/tex]

Answer: 20 sq. units .

Step-by-step explanation:

Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.

First we plot these points on coordinate plane, we get parallelogram ABCD.

By comparing the y-coordinate of B and C with A and D , we get

height = 2+2 = 4 units

Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units  

Area of parallelogram = Base x height

= 5 x 4 = 20 sq. units

Hence, the area of a parallelogram ABCD is 20 sq. units .

Answer:

Mean: 55.9

Median: 55

Mode: None

Step-by-step explanation:

First, find the mean by dividing the sum by the number of elements:

(72 + 58 + 62 + 38 + 44 + 66 + 42 + 49 + 76 + 52) / 10

= 55.9

Next, find the median by putting the numbers in order and finding the middle one:

38, 42, 44, 49, 52, 58, 62, 66, 72, 76

There is no middle number, so we will take the average of 52 and 58, which is 55.

Lastly, to find the mode, we have to find the number that occurs the most.

All of the numbers occur one time, so there is no mode.

Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]

The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between

the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].

Let consider x = rcosθ and y = rsinθ because x² + y² = r²;

Now, the double integral can be written in polar coordinates as:

[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]

[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]

[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]

Thus, the integral becomes:

[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]

∴

[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]  

[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]

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Answer:

Step-by-step explanation:

To find the ratio first find the diameter of the larger circle

Diameter of first circle = 6 inches

Diameter of second circle = 4 × diameter of the first circle

Which is

Diameter of second circle

= 4 × 6 = 24 inches

Area of a circle = πr²

r is the radius

Area of smaller circle

Diameter = 6 inches

Radius = 6 / 2 = 3 inches

Area = (3)² π = 9π in²

Area of larger circle

Diameter = 24 inches

Radius = 24 / 2 = 12 inches

Area = (12)²π = 144π in²

The ratio of the smaller circle to the larger circle is

[tex] \frac{9\pi}{144\pi} [/tex]

Reduce the fraction by 9π

That's

[tex] \frac{1}{16} [/tex]

We have the final answer as

Hope this helps you

Answer:

C. 1:16

Step-by-step explanation:

Area of a circle is:

[tex]\pi \times {r}^{2} [/tex]

Small circle Area:

radius = diameter/2

radius = 6/2 = 3

[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]

a = 28.27

Large circle 4 times larger diameter

6*4 = 24

diameter = 24

r = 24/2

r = 12

[tex]a \: = \pi {12}^{2} [/tex]

a = 452.39

area of large circle/ area of small circle

452.39/28.27 = 16.00

ratio is 1:16

A. 26%

There are 30% people who use both methods, Exercise near home or work and Exercise outdoor.

There are 46% people who prefer exercise near home or office rather than outdoor.

There are 40% people who prefer exercise outdoor rather than near home or office.

Then there are 30% people among them who use both methods. The remaining 26% people use one of the method.

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Answer:

Step-by-step explanation:

[tex]-3\left(x+1\right)=-3\left(x+1\right)-5\\\\\mathrm{Add\:}3\left(x+1\right)\mathrm{\:to\:both\:sides}\\\\-3\left(x+1\right)+3\left(x+1\right)=-3\left(x+1\right)-5+3\left(x+1\right)\\\\\mathrm{Simplify}\\\\0=-5\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{No\:Solution}[/tex]

Answer:

w = -46/5

Step-by-step explanation:

Answer:

w=-9.2

Step-by-step explanation:

7(w+8)=2w+10

7w+56=2w+10

7w-2w=10-56

5w=-46

w=-9.2

Answer:

[tex]\sqrt{51}[/tex] units.

Step-by-step explanation:

Point E is inside a rectangle ABCD.

Please refer to the attached image for the given statement and dimensions.

Given that:

Sides AE = 6 units

BE = 7 units and

CE = 8 units

To find:

DE = ?

Solution:

For a point E inside the rectangle the following property hold true:

[tex]AE^2+CE^2=BE^2+DE^2[/tex]

Putting the given values to find the value of DE:

[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]

this is a random sample because the instructor randomly selected the classes that she wants to use for her interview.

The  sampling method used is random sample.

To reach substantial inferences from your outcomes, you need to painstakingly conclude how you will choose an example that is illustrative of the gathering in general. A sampling method is the name for this. You can use one of two primary types of sampling methods in your research:

By using random selection in probability sampling, you can draw solid statistical inferences about the entire group.

You can easily collect data with non-probability sampling, which uses non-random selection based on convenience or other criteria.

Given English instructor randomly select 3 classes,

and  then interviews all students in those three classes to determine the average number,

Every member of the population has the same chance of being chosen in a straightforward random sample. The entire population should be included in your sampling frame.

You can use techniques that are entirely based on chance or tools like random number generators to carry out this kind of sampling.

The method used is Random sample method.

Hence, Random sample sampling is used.

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he would need about 5 more hits to make his average equal to that in 2021

128/501 = .255

The player needs 5 consecutive hits in order to raise his 2010 batting average to that of 2011.

An average of a list of data is the expression of the central value of a set of data. It is also defined as the ratio of summation of all the data to the number of units present in the list.

It is given that a professional player had 123 hits and 501 at-bats in 2010 and in 2011, he had 131 hits and 515 at-bats.

Also, the baseball player's batting average is equal to the number of hits divided by the number of at-bats.

Average in 2010 - 123/501 = 0.245 .

Average in 2011 - 131/515 = 0.254 .

Thus if he increases the number of shots to 5 then we have the total number of shots as 123 + 5 = 128 .

Therefore the batting average for 2010 becomes - 128/501 = 0.255 which matches the batting average of 2011.

Thus, the player needs 5 consecutive hits in order to raise his 2010 batting average to that of 2011.

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Answer:

A

f(x) = 1/4 x^2 + 3

Resultado

f(x) = x^2/4 + 3

x^2 + 12 = 4 f(x)

Forma alternativa

f(x) = 1/4 (x^2 + 12)

Raíces complejas

x = -2 i sqrt(3)

x = 2 i sqrt(3)

Answer:

The probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

Step-by-step explanation:

The complete question has the data of mean = 80 kg and standard deviation = 8kg

We have to find the probability between 72 kg and 88 kg

Since it is a normal distribution

(x`- u1 / σ/ √n) < Z >( x`- u2 / σ/ √n)

P (72 <x>88) = P ( 72-80/8/√1) <Z > ( 88-80/8/√1)

= P (-1<Z> 1) = 1- P (Z<1) - P (Z<-1)

= 1- 0.8413- (- 0.8413)= 1- 1.6826= 0.6826

So the probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

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▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

Step-by-step explanation:

Answer: D) 2 ohms and 2 ohms

The line cuts the X axis at [tex]x=3[/tex] and is parallel to the Y axis.

Thus the equation of the line is $\boxed{x=3}$

Answer:

The equation of the line is x = 3.

Step-by-step explanation:

When a line is parallel to the y-axis, its gradient will be undefined. There is no y-intercept and the line touches x-axis so the equation is x = 3.

Answer:

A) 64x + 285 = 605

B) 5 hours

Step-by-step explanation:

64x + 285 = 605

64x + 285-285 = 605 - 285

64x = 320

64x/64 = 320/64

x = 5

Double check

($605 Total - $285 parts) / $64 Hourly rate = Labor per hour

$320 Labor / $64 Hour = 5 hours

or 64x

Answer:

B: Add/subtract the same quantity to/from both sides

Next Question: Yes

Step-by-step explanation:

thats what the answer is dunno what else to tell you lol

Algebraic equations are mathematical equations that contain unknown variables.

2x - 1 = 5x .............Equation A

To get Equation B from A, we would subtract 2x from both sides of the equation.

2x - 2x - 1 = 5x - 2x

- 1 = 3x This is Equation B

2x - 1 = 5x  is equal to  -1 = 3x.

Hence, both Equation A and Equation B are equivalent expressions.

Therefore,

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Step-by-step explanation:

Just sub 4 into where n is

Answer:

y = sin(4(x+π/8)) + 1

Step-by-step explanation:

For a trigonometric equation of form

y = Asin(B(x+C)) + D,

the amplitude is A, the period is 2π/B, the phase shift is C, and the vertical shift is D (shifts are relative to sin(x) = y)

First, the amplitude is the distance from the center to a top/bottom point (also known as a peak/trough respectively). The center of the function given is at y=1, and the top is at y=2, Therefore, 2-1= 1 is our amplitude.

Next, the period is the distance between one peak to the next closest peak, or any matching point to the next matching point. One peak of this function is at x=0 and another is at x= π/2, so the period is (π/2 - 0) = π/2. The period is equal to 2π/B, so

2π/B  = π/2

multiply both sides by b to remove a denominator

2π = π/2 * B

divide both sides by π

2 = 1/2 * B

multiply both sides by 2 to isolate b

4 = B

After that, the phase shift is the horizontal shift from sin(x). In the base function sin(x), one center is at x=0. However, on the graph, the closest centers to x=0 are at x=± π/8. Therefore, π/8 is the phase shift.

Finally, the vertical shift is how far the function is shifted vertically from sin(x). In sin(x), the centers are at y=0. In the function given, the centers are at y=1, symbolizing a vertical shift of 1.

Our function is therefore

y = Asin(B(x+C)) + D

A = 1

B = 4

C = π/8

D = 1

y = sin(4(x+π/8)) + 1

Answer(s):

[tex]\displaystyle y = sin\:(4x + \frac{\pi}{2}) + 1 \\ y = -cos\:(4x \pm \pi) + 1 \\ y = cos\:4x + 1[/tex]

Explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{8}} \hookrightarrow \frac{-\frac{\pi}{2}}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = sin\:4x + 1,[/tex] in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{8}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle \frac{\pi}{8}\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{8}} = \frac{-\frac{\pi}{2}}{4}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = sin\:(4x + \frac{\pi}{2}) + 1.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, 2],[/tex] from there to [tex]\displaystyle [\frac{\pi}{2}, 2],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex] in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

D 70°F

Step-by-step explanation:

Difference between temperature in Hawaii and in South Dakota is 12°F - (-58°F) = 12°F + 58°F = 70 °F

Answer:

Jamal will have made 12 more T-shirts than Sean on the 6th day.

Step-by-step explanation:

1 day for Jamal - 6 T-shirts.                                                                                        1 day for Sean - 4 T-shirts.                                                                                               2 day for Jamal - 12 T-shirts.                                                                                                  2 day for Sean - 8 T-shirts.                                                                                                     3 day for Jamal - 18 T-shirts.                                                                                              3 day for Sean - 12 T-shirts.                                                                                               4 day for Jamal - 24 T-shirts.                                                                                                  4 day for Sean - 16 T-shirts.                                                                                                   5 day for Jamal - 30 T-shirts.                                                                                                5 day for Sean - 20 T-shirts.                                                                                             6 day for Jamal - 36 T-shirts.                                                                                                   6 day for Sean - 24 T-shirts.                                                                                           Number between 24 and 36 = 12.

Answer:

( x +4)^2 + ( y-7)^2 = 36

Step-by-step explanation:

We can write the equation of a circle as

( x-h)^2 + ( y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x- -4)^2 + ( y-7)^2 = 6^2

( x +4)^2 + ( y-7)^2 = 36

Answer:

(x+4)[superscript]2 + (y-7)[superscript]2 = 36

Answer:

1st, keep value of x in 1st equation

Step-by-step explanation:

-6(-2y-1)+2y=48

12y+6+2y=48

14y=48-6

y=42/14

y=3

Now putting value of y in equation ii)

x= - 2y-1

x= - 2×3-1

x= - 6-1

x= - 7

Therefore, x= - 7

y=3