Kenneth has entered a check payment of $350.25 in his checkbook. If the old balance was $545.95, what is his latest balance?
A.
$896.25
B.
$195.70
C.
$195

Answer:

5 feet.

Step-by-step explanation:

if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.

Answer:

2-3/-6-(-8)

= -1/2

Answer:

8 feet

Step-by-step explanation:

there's 12 inches in 1 foot so 12 x 8 = 96

The linear equation:

-28 = y/7

Can be solved by multiplying both sides by 7, to get y = -196

Here we want to solve the equation:

-28 = y/7

And we want to solve this for the variable y.

To do so, we need to isolate said variable in one side of the equation, now remember that we can multiply both sides of the equation by the same number.

Then we can multiply both sides by 7 so we get:

-28*7 = (y/7)*7

-196 = y

The correct option is the last one.

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Answer: θ≈18,553°

Step-by-step explanation:

[tex]\displaystyle\\sin\theta=\frac{7\ cm}{22\ cm} \\\\sin\theta=\frac{7}{22}\\\\\theta=arcsin\frac{7}{22} \\\\\theta\approx18.553^0[/tex]

Answer:99

Step-by-step explanation:

1/2 x18x11

99

The equations represent functions where x is the input and y is the output are y = 2x and x+y = 2

The 1st equation is x =2

Since there is no component of y and the value of x is fixed. So this is not the desired option.

The 2nd equation is y = 2

Since there is no component of x, and the value of y is fixed. So this is not the desired option.

The 3rd equation is y = 2x

In this equation, x is the input and y is the output. For different values of x, we will have different values of y.

Thus, this is the desired option.

The 4th equation is x =2y

In this equation, y is the input and x is the output. For different values of y, we will have different values of x.

The 5th equation is x+y = 2

So, x + y = 2

y = 2 - x

In this equation, x is the input and y is the output. For different values of x, we will have different values of y.

Thus, this is the desired option.

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A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4

Given,

24 inches on each of its three side. (See in attached picture)

Consider ADB,

As it is an equilateral triangle, BD = BC/2 = 12 inches

By Pythagoras theorem,

AB^2 = BD^2 + AD^2

24^2 = 12^2 + AD^2

24^2 – 12^2 = AD^2

576-144 = AD^2

432= AD^2

20.78= AD

Area = ½ (base * height)

       = ½ (24*20.78)

       = 249.4

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The area of the trapezoid is maximum when the fourth side be 20 inches.

Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.

By applying Pythagorean theorem,

[tex]c^2=a^2+b^2[/tex]

[tex]10^2=h^2+x^2[/tex]

[tex]100=h^2+x^2[/tex]

[tex]h^2=100-x^2[/tex]

[tex]h=\sqrt{100-x^2}[/tex]

Area of the trapezoid is,

[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]

By substituting  the values of h, b1, and b2 in the above equation,

[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]

[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]

If we take the derivative of both sides of the equation in relation to x, we get

[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]

[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]

[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

[tex]\frac {dA}{dx}=0[/tex]

[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

100-x²=x²+10x

2x²+10x-100=0

x²+5x-50=0

(x-5)(x+10)=0

If, x+10=0

x=-10

The above value is not accepted because it is a negative value,

If, x-5=0

x= 5

The value is accepted because it is positive value

The length of the trapezium which should be fourth is,

b₂=2x+10

b₂= 2(5)+10

b₂=20

The area of the trapezoid is maximum when the fourth side be 20 inches

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The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.

The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.

Using the SAS, the proof that shows both triangles are congruent is explained below.

Statements                        Reasons                                          

1. SR ≅ PR                          1. Given

2. SP bisects TQ               2. Given

3. TR ≅ QR                        3. Definition of bisection

4. ∠TRS ≅ ∠QRP              4. Vertical ∠s theorem

5. ΔTRS ≅ ΔQRP              5. SAS congruence theorem

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Answer:

To do percentages with fractions,

divide the numerator by denominator to get a decimal,

so for example, 12/40.

12/40 is 0.3 decimal, and then to make it percent,

we multiply by 100,

how does that work?

you move two places to the right because 100 has two zeros

so 0.3 would be 30,

therefore the percent of 12/40 would be 30%

number two same thing

33/60=0.55

0.55x100=55

so 55%

have a good day! <3

Answer:

Step-by-step explanation:

To solve the given problem first we need to find the equation for line then we have to find the intersection point on circle.

You will pick up a signal from the transmitter in 29% of the drive.

Given:

The radius is 53 mile.

The origin point of transmitter is .

Calculate the slope of line with point  and .

Substitute the value.

Write the general equation of line.

Now we got the equation of line,

Write the transmitter reach the area enclosed by the next circle.

Substitute the value of .

Thus, You will pick up a signal from the transmitter in 29% of the drive.

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c = 2.97r is the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost

Two variables have a proportional relationship if all the ratios of the variables are equivalent

In order to write an equation that describes the proportional relationship r, the number of reams purchased and c, the total cost, we need to write a proportional equation using the variables:

c α r                  (Note: α is the proportion symbol)

c = kr

k = c/r

Where k is the constant of proportionality

As shown in the image, you can see that 4 reams cost $11.88 and 6 reams cost $17.82

k = c/r

k = 11.88/4 = 2.97 or 17.82/6 = 2.97

c = kr

c = 2.97r

Therefore, the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost is c = 2.97r. Enter c = 2.97r in the box

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Step-by-step explanation:

1. in a parallelogram the opposite angles are equal.

so,

3x - 7 = x + 73

and

angle DAB = angle DCB = z - 3

3x - 7 = x + 73

2x - 7 = 73

2x = 80

x = 40

angle ADC = angle ABC = x + 73 = 40 + 73 = 113°

to get to z we need also to remember, as a quadrilateral shape the sum of all inner angles of a parallelogram is 360°.

so,

2×113 + 2×(z - 3) = 360

226 + 2z - 6 = 360

220 + 2z = 360

2z = 140

z = 70

angle DAB = angle DCB = z - 3 = 70 - 3 = 67°

Answer:

Step-by-step explanation:

By definition of a parallelogram, we know that the opposite angles are equal.

Thus, x+73=3x-7.

We can further use algebra and subtract by 3x and 73 on both sides.

We now have -2x=-80.

If we divide both sides by -2, then we get x=40.

We can plug x=40 back into 3x-7 and x+73, and we get 113 for both angles, which of course makes sense because they should be equal.

By definition of a parallelogram, we know that the angles of a parallelogram add up to 360, and that angle DAB = angle BCD = z-3.

This means that 113+113+z-3+z-3=360.

Combining like terms, we get 220+2z=360.

We can use algebra again, and subtract both sides by 220, getting 2z=140.

Dividing both sides by 2, we get z=70.

Because angle DAB=z-3, and z=70, we can plug in 70 for z, producing the result of angle DAB=67.

Answer:

0 + 0.30 + 0.08

Step-by-step explanation:

hope it helps :)

The domain of the function f(x) = 3x is (b) All positive integers less than or equal to 4

From the question, we have the following equation of the function that can be used in our computation:

f(x) = 3x

In this case, the notations are given as

x = Number of splits

f(x) = number of new roots in each split

From the question, we have

Splits = 4

This means that the maximum value of x is 4

The other values of x would be

x = 1, 2, 3, 4

This can be represented as

0 ≤ x ≤ 4

The interpretation of the above notation is all positive values less than or equal to 4

Hence, the domain value is option (b)

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Answer:

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

Given equation:

[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]

Simplify using the double angle identities:

[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]

[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]

[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]

[tex]\implies \tan x-2\sin x =0[/tex]

Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):

[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]

Multiply both sides by cos(x):

[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]

[tex]\implies \sin x-2\sin x \cos x=0[/tex]

Factor out sin(x) from the left side of the equation:

[tex]\implies \sin x(1-2 \cos x)=0[/tex]

Apply the zero-product property.

Case 1

[tex]\implies \sin x=0[/tex]

[tex]\implies x=\sin^{-1}(0)[/tex]

[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]

Case 2

[tex]\implies 1-2 \cos x=0[/tex]

[tex]\implies 1=2 \cos x[/tex]

[tex]\implies \cos x=\dfrac{1}{2}[/tex]

[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]

[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]

Solution

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

Answer:

yes it is???

Step-by-step explanation:

"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.

The true parameter must be properly and contextually stated.

We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.

Thus the correct statement is as mentioned above.

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The new mirror must have at least 81 cm² of the area.

The area of the square is defined as the product of the length and width.

As per the given question, we have

Dominic requires a new bicycle mirror. His old mirror was a square with a 9-cm side length.

He wants the replacement mirror to have an area that is as near to his previous bike mirror as feasible.

We have to determine the area of the previous bike mirror.

The area of the previous bike mirror = (side length)²

The area of the previous bike mirror = (9)² = 9 x 9

The area of the previous bike mirror = 81 cm²

So the new mirror must have greater than 81 cm² of area.

Thus, the new mirror must have at least 81 cm² of the area.

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Answer:

5 cm

Step-by-step explanation:

hope this helps

The probability that a randomly selected student majors in business or economics is 44.8%.

Let 'B' be the students of business.

P(B) = 35.1%

Let 'E' be the students of business.

P(E) = 12.3%

Thus,

P(E ∩ B) = 2.6%

P(E ∪ B) = probability for student majors in business or economics.

P(E ∪ B) = P(B) + P(E) - P(E ∩ B)

Put the values-

P(E ∪ B) = 35.1% + 12.3% -  2.6%

P(E ∪ B) = 44.8%

Thus, the probability that a randomly selected student majors in business or economics is 44.8%.

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Answer:

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

Three-digit integer in the form of abc.

Possible numbers for each digit

Let a = 5 or 7, then for a we have 2, for b and c 10 options:

Let b = 5 or 7, then for a we have 9 - 2 = 7, for b 2 and for c 10 options

Let c = 5 or 7, then for a we have 9 - 2 = 7, for b 10 - 2 = 8 and for c 2 options

Answer:

part b

y + 1 = 5/4(x - 2)  

part c

y - 5 = 3(x - 0) or y - 5 = 3(x)

Step-by-step explanation:

Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.

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The function g(X) will be of the form g(x) = |x/6| ,when stretched by a factor of 6.

The function is f(x)=|x| .

We know that for transformation of a function of the form horizontal stretch by a factor of 'a' is given by the g(x)= f(x/a)

So in this given function the horizontal stretch is by a factor of 6.

Therefore g(x) = f(x/6)

or, g(x) = |x/6|

In the graph attached the green represents the function f(x) while the red represents the function g(x).

A function transformation either "moves," "resizes," or "reflects" the graph of anything similar to the parent function. The following are the three main types of function transformations:

Dilation is the only one of these changes that modifies the size of the original shape; the other two just change its location.

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The unit rate for 96 kilometers in 3 hours  is 32 kilometer per hour.

What is unit rate?

A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given in the question,

96 kilometer in 3 hours,

In order to find unit rate we have to change given values in kilometers per hour.

Do, 96 kilometer = 3 hours

96/3 kilometer = 1 hour

Therefore, unit rate is 32 kilometer per hour.

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The solution for r in equation 5 + r = 6 - r,   r =1/2

The solution for z in equation  z - 16 = - 16,  z= 0

The solution for n in equation 7n - 7 = 0 ,    n= 1

(8) 5 + r = 6 - r

Step 1: Rearrange the equation by collecting the like terms

r +r=6-5

Step 2: Simplify r +r=6-5

2r = 1

Step 3: Divide both sides by 2

2r/ 2 =1/2

r =1/2

9) z - 16 = - 16

Step 1; Add 16 to both sides

z-16 +16 = -16 +16

z= 0

10) 7n - 7 = 0

To solve for n

Step 1: Add 7 to both sides

7n - 7 +7 = 0+7

7n =7

Step 2: Divide both side by 7

7n/7 =7/7

n= 1

Therefore, the solution for r in equation 5 + r = 6 - r, r =1/2

The solution for z in equation  z - 16 = - 16,    z= 0

The solution for n in equation 7n - 7 = 0,   n= 1

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Triangle ADC and ΔBDC are congruent.     then DE ≅ CE

What do you mean by congruent?

Given,

        AD ≅ BC

      ∠BCD ≅ ∠ADC

In triangle ADC and ΔBDC

                    AD ≅ BC    ( GIVEN )

      ∠BCD ≅ ∠ADC          ( GIVEN )

             DC = DC             ( Common line)

so  triangle ADC and ΔBDC are congruent.

             then DE ≅ CE

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The probability of spinning a 1 is the same for both spinners: False​

The spinners that complete the question are added as an attachment

From the attached figures, we  have

Spinner 1

Number of 1 = 1

Sections = 4

Spinner 2

Number of 1 = 2

Sections = 6

The probability of obtaining 1 is calculated as

P(1) = Number of 1/Sections

So, we  have

Spinner 1

Number of 1 = 1

Sections = 4

P(1) = 1/4

Spinner 2

Number of 1 = 2

Sections = 6

P(1) = 2/6

By comparison

1/4 and 2/6 do not have the same value

Hence. it is false that the probability of spinning a 1 is the same for both spinners

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