Grace's mom gave her $15.00 to buy school supplies. Grace needs to buy 3 mechanical pencils and some notebooks. If each mechanical pencil costs $1.75 and each notebook costs $2.99, how many notebooks can Grace buy using only the money her mom gave her? 2 notebooks 3 notebooks 4 notebooks 5 notebooks

Answer:

Simplifying

41 = 12d + -7

Reorder the terms:

41 = -7 + 12d

Solving

41 = -7 + 12d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-12d' to each side of the equation.

41 + -12d = -7 + 12d + -12d

Combine like terms: 12d + -12d = 0

41 + -12d = -7 + 0

41 + -12d = -7

Add '-41' to each side of the equation.

41 + -41 + -12d = -7 + -41

Combine like terms: 41 + -41 = 0

0 + -12d = -7 + -41

-12d = -7 + -41

Combine like terms: -7 + -41 = -48

-12d = -48

Divide each side by '-12'.

d = 4

Simplifying

d = 4

Answer:

5/3

Step-by-step explanation:

it should be y/x

you can count 5 up and 3 over

Answer:

8/5

Step-by-step explanation:

You can use the formula [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex] with a pair of points [tex](x_{1},y_{1})[/tex][tex](x_{2},y_{2})[/tex]. We can use points (1,4) and (-4,-4). Plugging in the equation we get (4-(-4))/(1-(-4)), which simplifies to 8/5, which is the slope.

Answer:

0.125 miles per gallon.

Step-by-step explanation:

After 200 gallons used the freight train has traveled 25 miles. This means that we need to divide both sides by 200 to get a singular gallon's worth of miles traveled. 200/200 is 1, and 25/200 is 0.125.

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Extra

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IF it were how many gallons per mile, you would divide both answers by 25 resulting in 8 gallons per mile.

Answer:

It's the first option.

Step-by-step explanation:

The line which rises to the right has a slope of 1 and a y-intercept of -6.

It's equation is y = x - 6.

The one which rises to the left has slope -1 and y-intercept -2.

It's equation is y = -x - 2  or x + y = -2.

The solution is at the point where the 2 lines cross - that is (2, -4).

Answer:

The number of distinct triangles that can be drawn using the dots = 6

Step-by-step explanation:

The parameters given are;

Two rows of three evenly spaced dots

To form a triangle, two dots will be selected from 1 row while the third dot will be selected from the other row

The number of ways of selecting the dots are therefore;

₃C₂ × ₃C₁ = 3 × 3 = 9 triangles

The same procedure can be done from the top row to give another 9 triangles

Which gives the total number of triangles = 18 triangles

The number of distinct triangles are found as follows;

Given that triangles obtained from the top row are similar to those of the bottom row, we reduce the range from which the distinct triangles can be found to 19 - 9 = 9 triangles

Of the 9 triangles formed by one dot on top and two dots on the bottom, the two adjacent dots of the three dots which are on the left and on the right of the lower row of dots, form the same three triangles with the three dots on the top row

Therefore, since there are 3 sets of two dots forming 9 triangles, each pair of dots can form 3 triangles, and as mentioned, 2 pairs of dots of the 3 pairs form the same triangles making the distinct triangle = 9 - 3 = 6.

Answer:

[tex]x = 500[/tex]

Step-by-step explanation:

Given

[tex]log20x^3 - 2logx = 4[/tex]

Required

Solve for x

[tex]log20x^3 - 2logx = 4[/tex]

Using law of logarithm which says;

[tex]nlogx = logx^n[/tex]

The expression becomes

[tex]log20x^3 - logx^2 = 4[/tex]

Also, using laws of logarithm which says:

[tex]loga - logb = log\frac{a}{b}[/tex]

The expression becomes

[tex]log(\frac{20x^3}{x^2}) = 4[/tex]

[tex]log(20x) = 4[/tex]

Also, using laws of logarithm which says

[tex]If\ loga = b\\then\ a = 10^b[/tex]

The expression becomes

[tex]20x = 10^4[/tex]

[tex]20x = 10000[/tex]

Divide through by 20

[tex]\frac{20x}{20} = \frac{10000}{20}[/tex]

[tex]x = \frac{10000}{20}[/tex]

[tex]x = 500[/tex]

Answer:

500

Step-by-step explanation:

Answer:

The volume of the cone is 1006.9in³

Step-by-step explanation:

Given

[tex]Height = 18.8\ in[/tex]

[tex]Diameter = 14.3\ in[/tex]

Required

Calculate the volume;

The volume of a cone is calculated as thus;

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where V represents volume; r represents radius; and h represents height

The radius is calculated as thus;

[tex]r = \frac{1}{2}Diameter[/tex]

[tex]r = \frac{1}{2} * 14.3[/tex]

[tex]r = 7.15[/tex]

Substitute [tex]r = 7.15[/tex]; [tex]h = 18.8[/tex] and [tex]\pi = \frac{22}{7}[/tex]

[tex]V = \frac{1}{3} \pi r^2h[/tex] becomes

[tex]V = \frac{1}{3} * \frac{22}{7} * 7.15^2 * 18.8[/tex]

[tex]V = \frac{1}{3} * \frac{22}{7} * 51.1225 * 18.8[/tex]

[tex]V = \frac{22* 51.1225 * 18.8}{3 * 7}[/tex]

[tex]V = \frac{21144.266}{21}[/tex]

[tex]V = 1006.86980952[/tex]

[tex]V = 1006.9\ in^3[/tex] (Approximated)

Hence, the approximated volume of the cone is 1006.9in³

Answer:1006.5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.

Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.

3^2 is 9 so you get 18

the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18

Hope this helps!

Answer:

a) x = 128 degrees

b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Step-by-step explanation:

Given:

attached diagram

ABC is a straight line

Solution:

a) Find x

ABC is a straight line

angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.

x is the central angle of the arc APD

so angle ABD is the inscribed angle which equals half of the arc angle =>

angle ABD = x/2 = 64 degrees

Solve for x

x/2 = 64

x = 2*64

x = 128 degrees

b.

Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Answer:

Option (A)

Step-by-step explanation:

Parent function of the function graphed is,

G(x) = x²

Graph shows the vertex of the given parabola is at (3, 3).

Vertex form of a parabola is,

F(x) = a(x - h)² + k

where (h, k) is the vertex.

By substituting the coordinates of the vertex in the equation,

F(x) = a(x - 3)² + 3

Since the given parabola is opening upwards, value of 'a' will be positive.

So the equation will be,

F(x) = 2(x - 3)² + 3

Therefore, from the given options, equation given in Option (A) matches the answer.

Answer:

A is the correct answer.

Step-by-step explanation:

Answer:

B) 128.3 square yards

Step-by-step explanation:

A = (n/360 deg)(pi)r^2

where n = central angle of sector.

A = (75/360)(3.14159)(14 yd)^2

A = 128.3 yd^2

Answer:

B. 128.3 yards

Step-by-step explanation:

Area of a Sector Formula: A = ∅/360πr²

Simply plug in our variables:

A = 75/360(π)(14)²

A = 5π/24(196

A = 128.3

Answer:

Company B

Step-by-step explanation:

We would use z score formula

z = (x - μ) / σ

x = raw score

μ = mean

σ = Standard deviation

let x = 260 with the mean μ1 = 276 and standard deviation σ = 5.8

let x = 260 with the mean μ2 = 252 and standard deviation σ = 3.4

z1 = (x- μ1) / σ = (260- 276) / 5.8 = -2.7586206897

z2 = (x2 - μ) / σ = (260 -252) / 3.4= 2.3529411765

Comparing the two z scores, we can see that company B has the probability of producing 260 nails because it has a positive z score of approximately 2.35 compared to company A with a z score of -2.76.

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value [tex]=x+30-30=x[/tex], it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]

Afer 40% increase.

New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.

4. A 75% increase followed by a 33% decrease

New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

A 100% increase followed by a 50% decrease

A $30 increase followed by a $30 decrease

55% decrease followed by a 25% increase

A 20% decrease followed by a 40% increase

A 75% increase followed by a 33 1/3% decrease

Answer:

No

Step-by-step explanation:

The question is:

Are 3/5 and 6/25 equivalent fractions?

Multiply the first fraction by 5/5:

3/5 * 5/5 = 15/25

3/5 is equivalent to 15/25

15/25 is not equal to 6/25.

Answer: No

Answer:

Step-by-step explanation:

x + 2x + 4x = 49

7x = 49

x = 7

2(7)= 14 hours he worked on Wednesday

Answer:

? = 78

Step-by-step explanation:

Use similar triangles.

26/12 = (26 + ?)/48

13/6 = (26 + ?)/48

6(26 + ?) = 13 * 48

156 + 6? = 624

6? = 468

? = 78

Answer:

The missing segment is equal to 78

Step-by-step explanation:

Using the similarity of triangles:

[tex]x=?[/tex]

[tex]$\frac{x+26}{48}=\frac{26}{12} $[/tex]

[tex]12(x+26)=48 \cdot 26[/tex]

[tex]12x+312=1248[/tex]

[tex]12x+312=1248[/tex]

[tex]12x=936[/tex]

[tex]x=78[/tex]

Answer:

The graph now opens in the opposite direction. The y intercept is shifted up 4.

Step-by-step explanation:

F(x) = 2x^2-8

F(X)= -2x^2-4

We know that the graph is reflected over the y-intercept becuase of the negative sign in the second equation ( F(X)= -2x^2-4)

We know that the intercept is shifted up four, because the number decreased from 8 to 4, and the graph is reflected.

Attacthed is both of the equations graphed to help you visualize this shift!

Answer:

1

Step-by-step explanation:

You only need two points to find the slope.

Let's use (1,7) and (2,8).

The formula for slope is (y2-y1)/(x2-x1)

Let's plug the values in:

(8-7)/(2-1) = 1.

So, the slope is 1.

Answer:

The answer should be 20.

Step-by-step explanation:

First, you need to understand the abbreviated list: PEMDAS. I'm not sure if you guys learned this or not, but it helps to know when solving problems like this.

So, if you don't know: PEMDAS is a list of what order you would need to start with when solving a problem. The order is Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

With that in mind, we'll start by looking at the numbers in the numerator of this fraction. (Doesn't matter if you start with the numerator or denominator first.)

You want to start with the numbers in the parentheses as that is the first letter in the PEMDAS phrase.

[tex](7-6.35) = 0.65[/tex]

Now, we have division and an addition sign next. According to PEMDAS, you want to start with Division before you Add. So, you will end up having a 10 in the numerator. (I'm assuming you can use a calculator for this, so I'm not showing how to divide the decimals.)

[tex]\frac{(0.65)}{6.5}+9.9=0.1+9.9 =10[/tex]

Save that number somewhere for now since we will have to come back to it later. For the denominator, we have a set of parentheses that the problem wants us to focus on so, ignore the [tex]7\frac{1}{24}[/tex] for now.

Start with the first set of numbers that have the division sign in between.

[tex]\frac{1.2}{36} =0.03333[/tex]

Don't add just yet after getting this number. You want to divide the 1.2 and [tex]\frac{1}{4}[/tex] since Division needs to be done first before Adding or Subtracting.

[tex]\frac{1.2}{\frac{1}{4} }=4.8[/tex]

The resulting numbers in the parentheses should look like this now (we're still ignoring the [tex]7\frac{1}{24}[/tex] at the end after the parentheses):

[tex](0.03333+4.8-1\frac{5}{16})=3.520833333[/tex]

This expression is also the same as this if you wanted to change the fraction at the end of the parentheses:

[tex](0.03333+4.8-\frac{21}{16})=3.520833333[/tex]

Now you can finally take this number and divide it by [tex]7\frac{1}{24}[/tex] or [tex]\frac{169}{24}[/tex].

[tex]\frac{3.520833333}{\frac{169}{24} }=0.5[/tex]

These are really big numbers when you are dividing so hopefully you don't have to solve this all out in your head or by paper. Now, remember that 10 we got from the numerator earlier? We can finally use that here where we have that as our numerator and 0.5 as our denominator.

[tex]\frac{10}{0.5} =20[/tex]

This gives you the final answer of 20.

Answer:

didnt understand the quedtion clearly

Answer:

Let's use Pythagorean Theorem which states:

6² + 10² = x²

36 + 100 = x²

136 = x²

x = ± 2√34

Since the side lengths of a triangle cannot be negative, x = -2√34 is an extraneous solution which means that x = 2√34.

Answer:Answer:

Let's use Pythagorean Theorem which states:

6² + 10² = x²

36 + 100 = x²

136 = x²

x = ± 2√34

Since the side lengths of a triangle cannot be negative, x = -2√34 is an extraneous solution which means that x = 2√34.

Read more on Brainly.com - https://brainly.com/question/17033938#readmore

Step-by-step explanation:

Answer:

Step-by-step explanation:

In general, the graph of an n-th degree function can make n-1 turns. However, in specific cases, the number of turns is limited by the number of real zero-crossings of the derivative.

__

1. This 5th-degree function can have at most 4 turns. However, the derivative, f'(x) = 5x^4 -3, has only two (2) real zeros. Hence the graph of this function can only have 2 turns.

__

2. This 7th-degree function can have at most 6 turns. However, the derivative, f'(x) = -7x^6 -35x^4-12x^2, has an even-multiplicity root at x=0 only. The derivative never crosses 0. Hence the graph makes no turns.

Answer:

A

Step-by-step explanation:

it right on edge

Answer:

A.

Step-by-step explanation:

Did the unit test in edge and got 100

Answer:

Yes, he will have enough paint to cover the tank with one layer of paint.

Step-by-step explanation:

We are given that Tublu buys a cylindrical water tank of height 1.4 m and diameter 1.1 m to catch rainwater off his roof. He has a full 2 liters tin of paint in his store and decides to paint the tank (not the base).

He uses 250 ml to cover 1 [tex]\text{m}^{2}[/tex].

From the question, it is clear the area of the tank which needs to be painted is the lateral surface area (because the base is not included).

The lateral surface area of the cylinder = [tex]2\pi rh[/tex]

where, r = radius of the cylinder =  [tex]\frac{\text{Diameter}}{2}[/tex]  = [tex]\frac{1.1 }{2}[/tex] = 0.55 m

           h = height of the cylinder = 1.4 m

           [tex]\pi[/tex] = 3.142 (given)

So, the lateral surface area of a cylindrical water tank = [tex]2 \times 3.142 \times 0.55 \times 1.4[/tex]

                                                                                         = 4.84 [tex]\text{m}^{2}[/tex].

Now, it is given in the question that; Tublu uses 250 ml to cover 1 [tex]\text{m}^{2}[/tex] area, this means that;

To cover 4.84 [tex]\text{m}^{2}[/tex] area, he will use paint = [tex]4.84 \times 250[/tex] = 1210 ml

Since he has a full 2 liters tin of paint in his store which is equal to 2000 ml but he need only 1210 ml of paint.

This means that yes, he will have enough paint to cover the tank with one layer of paint.

Answer:

-19.43

Step-by-step explanation:

Withdrawals are negative

Answer:

377 choices

Step-by-step explanation:

The following values were given in the question:

The restaurant offered

6 choices of appetizer

8 choices of main meal

5 choices of dessert.

We are also told in the question that the customer can choose to eat just one course, or two different courses, or all three courses.

Let us represent each choice by :

A = Appetizer = 6

B = Main meal = 8

C = Dessert = 5

a) The 3 choices together

ABC=6 × 8 × 5=240 choices

b) AB= Appetizer and Main meal

= 6 × 8 = 48 choices

c) AC= Appetizer and Dessert

= 6 × 5 = 30 choices

d) BC = Main meal × Dessert

= 8 × 5 = 40 choices

e) A,B,C = the customer having each of the choices only

Appetizer + Main meal + Dessert

= 6 + 8 + 5

= 19 choices

The number of possible meals is calculated as:

240 choices + 48 choices + 30 choices + 40 choices + 19 choices

= 377 choices

Answer:

The length of the missing segment is 36

Step-by-step explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]

[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]

Cross Multiply

[tex]20 * (24 + x) = 24 * 50[/tex]

[tex]20 * (24 + x) = 1200[/tex]

Divide both sides by 20

[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]

[tex](24 + x)= \frac{1200}{20}[/tex]

[tex]24 + x= 60[/tex]

Subtract 24 from both sides

[tex]24 - 24 + x = 60 - 24[/tex]

[tex]x = 60 - 24[/tex]

[tex]x = 36[/tex]

Hence, the length of the missing segment is 36

Answer:

[tex]C. \[/tex]   [tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]

Step-by-step explanation:

Given

[tex]x = 2[/tex]

[tex]y = 5[/tex]

Required

[tex]\frac{1}{2}x^3 + 3.4y[/tex]

Substitute 2 for x and 5 for y;

The expression becomes

[tex]=\ \frac{1}{2} * 2^3 + 3.4 * 5[/tex]

Multiply 3.4 by 5

[tex]=\ \frac{1}{2} * 2^3 + 17[/tex]

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

[tex]2^3 = 2 * 2 * 2 = 8[/tex]

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

[tex]=\ \frac{1}{2} * 8 + 17[/tex]

[tex]=\ \frac{8}{2} + 17[/tex]

[tex]=\ 4 + 17[/tex]

[tex]=\ 21[/tex]

Hence;

[tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]

Answer:

radius

Step-by-step explanation:

That "fixed distance" is the 'radius' of the circle.