Simplify the expression by rationalizing the denominator
[tex] \frac{7}{ \sqrt{2} } [/tex]
​

The heaviest bag has (1 + 1/8) lb more than the lightest bag.

By looking at the histogram, we can see that the heaviest bag weighs:

M = (5 + 1/2) lb

The lightest bag weighs:

m = (4 + 3/8) lb

Now we need to take the difference between these masses:

M - m =  (5 + 1/2) lb -  (4 + 3/8) lb = (5 - 4) lb + (1/2 - 3/8) lb

M - m = 1 lb + (4/8 - 3/8)lb = (1 + 1/8)lb

This means that the heaviest bag has (1 + 1/8) lb more than the lightest bag.

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It’s Profit Just took the quiz

Answer:

700 joules

Step-by-step explanation:

Basically,

The KE formula is this KE=1/2mv^2

So we substitute the mass for m and the meters per second for v (velocity)

[tex]\frac{1}{2} (14)(10^2)[/tex]

Use PEMDAS, one half times 14 is 7

10 squared is 100,

100*7 = 700

Thanks me later :)

Answer:

The answer is 600

Step-by-step explanation:

V = A(h/3)

Answer:

the answer is c

Step-by-step explanation:

Answer:

∠SRP and ∠QRP

∠TUR and ∠VUR

Step-by-step explanation:

Adjacent angles are angles that share a common side and have the same vertex. Here you need to see if each pair share a side and start at the same point.

∠SRP and ∠QRP: These are adjacent because they share the same vertex and side

∠TUR and ∠VUR: These are adjacent because they share the same vertex and side

∠QRP and ∠VUW: These are not adjacent because they do not share the vertex, only share a common side

∠TUR and ∠SRU: These are not adjacent because they do not share the vertex, only share a common side

Answer:

10 Male

16 Female

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

14 out of 105= 7.5

4 out of 30= 7.5

Both numbers, 14 and 4, have the same ratio.

There are 14 small breed dogs in the shelter.

The question involves using proportional reasoning to predict the number of small breed dogs in a shelter. From the given sample of 30 dogs, 4 are classified as small breeds. To find the predicted number of small breeds in the entire shelter, we set up a proportion based on the sample proportion:

4 small dogs out of 30 total dogs (sample) = x small dogs out of 105 total dogs (shelter).

Solving for x gives us the predicted number of small breed dogs:

(4/30) * 105 = x

Calculate the value of x:

x = (4* 105) / 30

x = 420 / 30

x = 14

Therefore, based on the sample, we would predict that there are 14 small breed dogs in the shelter.

Answer:

59 is an outlier in the numbers, which increased the average of the toys.

Answer:

A) The volume of figure 1 is 45 cm³ greater than the volume of figure 2

Step-by-step explanation:

Let's start by calculating the volumes of both figures

Figure 1

Rectangular prism

V = Bh

V = (15*6)(5)

V = (90)(5)

V = 450 cm³

Triangular prism

V = Bh

V = 1/2(3*15)(6)

V = 1/2(45)(6)

V = 1/2(270)

V = 135 cm³

Add them together, you get 585 cm³

Figure 2

Rectangular prism

V = Bh

V = (6*15)(5)

V = (90)(5)

V = 450 cm³

Rectangular pyramid

V = 1/3 Bh

V = 1/3 (15*6)(3)

V = 1/3 (90)(3)

V = 1/3 (270)

V = 90 cm³

Add them together, you get 540 cm³

Subtract 540 from 585 and get 45

Answer:

A) The volume of figure 1 is 45 cm³ greater than the volume of figure 2

Step-by-step explanation:

Answer:

-144 = 18

Step-by-step explanation:

1). 24xy = 6y

  x = -2; y = 3

  24(-2)(3) = 6(3)

   -144 = 18

Answer:

The answer is 10

Step-by-step explanation:

Equation to find the hypotenuse (c) is [tex]\sqrt{a^{2} +b^{2} }[/tex]

[tex]5^{2}[/tex] x [tex]2^{2}[/tex] = 100 (which is your [tex]c^{2}[/tex])

[tex]\sqrt{100}[/tex] = 10

Answer:

x= [tex]-5+2i, -5-2i[/tex] aka No Real Solution

Answer:

The answer is -3/10

Step-by-step explanation:

Answer:

-0.3 or -[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

Separate the squares making it:

[tex]-\frac{\sqrt{9} }{\sqrt{100}}[/tex]

Square root them:

[tex]\frac{3}{10}[/tex]

Don't forget the negative

[tex]-\frac{3}{10}[/tex]

Answer: I need to know the number for the slope. I know the y-intercept, which is b, but I need to know m (the slope) I can give you y = mx+6.

Step-by-step explanation:

Answer: 109/10

Step-by-step explanation:

1. Find the GCD (or HCF) of numerator and denominator

GCD of 109 and 10 is 1

2. Divide both the numerator and denominator by the GCD

109 ÷ 1

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

10 ÷ 1

3. Reduced fraction:  

109

-----------

10

Therefore, 109/10 simplified is 109/10

Answer:

(4, 0) and (6, 0)

Step-by-step explanation:

The function that we have is:

[tex]g(x)=x^2-10x+24[/tex]

This is the function of a parabola.

to find the points where the function crosses the x-axis, we need to find the values of x for which g(x) (which is the value of the y-axis) is equal to zero.

so we need [tex]g(x)=0[/tex] for the function to be crossing the x-axis.

Thus our equation becomes:

[tex]x^2-10x+24=0[/tex]

and we can solve this equation with the quadratic formula or by factoring.

I will sove by factoring:

To factor this type of equations we need to find 2 number that satisfy the following:

In this case those 2 number are: -6 and -4 because:

(-6)(-4)=+24

-6 - 4 = -10

Thus we arrange our factored equation as follows:

from [tex]x^2-10x+24=0[/tex] through factoring we get:

[tex](x-6)(x-4)=0[/tex]

and because of the zero factor property (if two things when multiplied result in zero one of them or both must be zero), thus our x values are:

[tex]x-6=0\\x=6\\[/tex]

and

[tex]x-4=0\\x=4[/tex]

thus, our points are those with and y coordinate of 0 and an x coordinate of 6 and 4:

(4,0) and (6,0)

Answer:

y=

Step-by-step explanation:

16²=256 sooo....

12y^2=256

6y*6y=256

find what y equals

Answer:

B

Step-by-step explanation:

E2021

Answer:

13.4 feet

Step-by-step explanation:

a²+b²=c²

12²+6²=c²

144+36=[tex]\sqrt{180}[/tex]

=13.4

The length of the cable is 13.416 feet.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have one end of the cable is attached to the top of a flagpole.

The other end is attached 6 feet away from the base of the pole.

The flagpole height = 12 feet

As we can see in the figure it is a right angle triangle in which the:

The length of the base of the right angle triangle b = 6 feet

The length of the perpendicular l = 12 feet

From the Pythagoras theorem:

[tex]\rm Hypotenuse^2 = Base^2+Perpendicular^2[/tex]

Let's suppose the length of the cable is x feet

[tex]\rm x^2 = 6^2+12^2[/tex]

[tex]x^2 = 36+144 \Rightarrow 180[/tex]

[tex]\rm x = \sqrt{180}[/tex]

x = 13.416 feet

Thus, the length of the cable is 13.416 feet.

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Answer:

Step-by-step explanation:

0.34 x 100 / 100

= 34 / 100

Reduce the fraction:

34/100 by 2

2 x 17 = 34

2 x 100 = 50

= 17/50

^ These are the lowest terms.

Answer:

17/50

Step-by-step explanation:

First, write as a fraction :

34/100 since it is thirty-four hundredths

then, simplify by finding GCD(greatest common divisor):

34 divided by 2=17; 100 divided by 2=50 so the fraction becomes:

17/50 in simplest form.

Answer : The percentage error will be, 45.5 %

Step-by-step explanation :

To calculate the percentage error, we use the equation:

[tex]\%\text{ error}=\frac{|\text{Experimental value - Accepted value}|}{\text{Accepted value}}\times 100[/tex]

We are given:

Experimental value = 16 inches

Accepted value = 11 inches

Now put all the given values in above equation, we get:

[tex]\%\text{ error}=\frac{|16-11|}{11}\times 100\\\\\%\text{ error}=45.5\%[/tex]

Hence, the percentage error will be, 45.5 %

Answer:

D. 31

Step-by-step explanation:

To find the mean of any group of numbers, you simply add up all the numbers and then divide by how many numbers there are.

Using a calculator or a pencil, add the following:

27 + 28 + 30 +28 + 28 + 31 + 29 + 33 + 28 + 28 + 31 + 33 + 41 + 41 + 25

= 461

The last step is to divide 461 by 15:

461/15 = 30.73

Round 30.73 to the nearest whole number and you get D. 31

Answer:

5/6th

Step-by-step explanation:

Board:

Width = 3 feet = 3*12 = 36 inches

Height = 1 foot = 1*12 = 12 inches

36 in (board width) / 2 in (posit width) = 18

12 in (board height) / 2 in (posit height) = 6

Area = base * height

Area = 18 post-its wide * 6 post-its height = 108 post-its

Answer:16

Step-by-step explanation:I think

Answer:

f^-1(x)= 9x+117

Step-by-step explanation:

hello :

let f(x) = y  so : y = 1/9 x-13

calculate : x       you have : 1/9x= y+13  so : x= 9(y+13)=9y+117

If f(x)=1/9x-13, then f^-1(x)= 9x+117

Probability of a the number will less than 4 is  [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

Given,

A die will be rolling.

To find the probability of a the number will less than 4.

Formula

Probability of an event = Number of possible outcomes ÷ Total number of outcomes

Here,

Less than 4 means =1,2,3 = 3 times

Total number of outcomes = 6

Hence,

Probability of a the number will less than 4 = [tex]\frac{3}{6} = \frac{1}{2}[/tex]

Answer:

4x(2x+3)(2x−3)

Step-by-step explanation:

Factor 16x3−36x

16x3−36x

=4x(2x+3)(2x−3)

Look at the attached picture ⤴⤴

Hope this will help u...

Answer:

6361.6 grams

Step-by-step explanation:

A chef at a restaurant uses 14 pounds of butter each day

Given;

16 ounces per pound

And

28.4 grams per ounces

Converting 14 pounds to gram;

14 pounds × 16 ounces/pound = 224 ounces

Then;

224 ounces × 28.4 grams/ounce = 6361.6 grams

The correct use of conversion factors will result in the cancellation of the unwanted units and retention of the desired unit.

Conversion factors are essential in unit conversions, allowing us to switch from one unit of measurement to another within the same system, such as U.S. customary units or the SI unit system. To use conversion factors effectively, one must ensure that the unit of measure they wish to convert from or to is correctly positioned in the conversion factor equation. For instance, when converting meters to centimeters, a factor of 1 cm/10-2 m or 100 cm/1 m is used because 'centi' means 10-2 in the SI unit system.

It is important to keep track of units being canceled during the conversion. If you have units in the numerator and denominator that are the same, they will cancel out, leaving only the desired unit. In the process of conversion, if the unit you want to convert is in the denominator of the original quantity, the conversion factor should have that unit in the numerator.

Choosing the right conversion factor and accurately performing the calculations are crucial. A proper conversion factor will cancel out unwanted units. Using an incorrect conversion factor without an opposing unit to cancel out will leave an unwanted unit in your answer, indicating an error in the process.

Dimensional analysis, which often involves conversion factors, simplifies the process of converting units and ensures that measurements within calculations are consistent. This technique is fundamental for scientific calculations and everyday applications, such as determining the appropriate unit to measure large volumes or distances.