Yesterday grace drove 41 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

108,864

Step-by-step explanation:

The difference between each value is x6, so you times the number by 6 to get the next number of the sequence :)

Answer:

135%

Step-by-step explanation:

The decimal 1.35 equals 135%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 1.35 × 100 = 135% (answer).

➥ The ease way:

1) Move the decimal point two places to the right: 1.35 → 13.5 → 135.

2) Add a % sign: 135%

Answer: 135%

Answer:

135%

Step-by-step explanation:

1.35 · 100 = 135%

The number of elements that are common to S and T are 668 elements ,

the correct option is (d) .

In the question ,

it is given that ,

the set S is the set of 2005 positive multiple of 4

that is S = {4,8,12,16,....}

and the set T is the set of 2005 positive multiple of 6

that is T = {6,12,18,24,....}

and since the least common multiple , LCM of 4 and 6 is = 12,

So , elements that are common to set  S and T must be multiples of 12.

Since,  4 × 2005 = 8020 and 6 × 2005 = 12030,

the several multiples of 12 that are in set T won't be in set S,

but all multiples of 12 that are in set S will be in set T.

So we have to find the number of multiples of 12 that are in set S.

and since 4 × 3 = 12, that means every 3rd element of set S will be a multiple of 12.

which is = 2005/3 = 668 .

Therefore , there are 668 elements that are common .

The given question is incomplete , the complete question is

Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. how many elements are common to S and T ?

(a) 166 (b) 333 (c) 500 (d) 668 (e) 1001

Learn more about Common Elements here

https://brainly.com/question/17009142

#SPJ4

Answer:

7

Step-by-step explanation:

Step 1:

a + 6 = 3a - 8     Equation

Step 2:

6 = 2a - 8       Subtract a on both sides

Step 3:

14 = 2a      Add 8 on both sides

Step 4:

14 ÷ 2     Divide

Answer:

a = 7

Hope This Helps :)

Answer:

The slope is 5/12

Step-by-step explanation:

To find the slope between any two points, we can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Where (x₁, y₁) and (x₂, y₂) are our two points.

We have the two points (-9, 1) and (3, 6).

Let’s let (-9, 1) be (x₁, y₁) and let (3, 6) be (x₂, y₂). Substitute appropriately:

\(\displaystyle m=\frac{6-1}{3-(-9)}\)

Evaluate:

\(\displaystyle m=\frac{5}{12}\)

So, the slope of the line that contains the two points (-9, 1) and (3, 6) is 5/12.

Answer: x=117

Step-by-step explanation:

180-63=117 because of supplementary angles.

Answer:

sixteen centimeter! hope this helps!

Answer:

Step-by-step explanation:

Assuming that "f" represents the value of the car as a function of time in months, we can use the formula for exponential decay to calculate the value of the car at different times:

f(t) = initial value x (1 - decay rate)^time

In this case, the initial value is $36,900, and the decay rate is 21% per year, which is equivalent to 1.75% per month (since there are 12 months in a year). Therefore, the decay rate can be expressed as 0.0175.

To calculate the value of the car after a certain number of months, we can substitute the time (in months) into the formula for f(t). For example:

At f(1) month:

f(1) = $36,900 x (1 - 0.0175)^1 = $36,209.63

So the value of the car after 1 month of depreciation is approximately $36,209.63.

At f(6) months:

f(6) = $36,900 x (1 - 0.0175)^6 = $31,573.13

So the value of the car after 6 months of depreciation is approximately $31,573.13.

At f(8) months:

f(8) = $36,900 x (1 - 0.0175)^8 = $29,784.62

So the value of the car after 8 months of depreciation is approximately $29,784.62.

Note that these calculations are based on the assumption that the depreciation rate remains constant over time. In reality, the depreciation rate may change due to various factors, such as wear and tear, market conditions, and maintenance. Therefore, these values should be considered as estimates only.

The dimensions of the closed cylinder that maximize its volume are radius=25 cm and height=40 cm. The maximum volume is 62,500 cubic cm.

Given that the total surface area of the closed cylinder is 5000 cm^2, we can write the equation for the total surface area as:

2πrh + 2πr^2 = 5000

We want to find the dimensions that maximize the volume of the cylinder. The volume of a cylinder is given by:

V = πr^2h

We can use the equation for the total surface area to solve for h in terms of r:

h = (5000 - 2πr^2) / (2πr)

Substituting this expression for h into the equation for the volume, we get:

V = πr^2[(5000 - 2πr^2) / (2πr)]

Simplifying this expression, we get:

V = (2500πr - πr^3)

To find the maximum volume, we take the derivative of V with respect to r and set it equal to zero:

dV/dr = 2500π - 3πr^2 = 0

Solving for r, we get r=25 cm.

We can then substitute this value of r into the expression for h to get h=40 cm.

Therefore, the dimensions of the cylinder that maximize its volume are radius=25 cm and height=40 cm.

Substituting these values into the equation for the volume, we get:

V = π(25)^2(40) = 62,500 cubic cm.

To verify that this is a maximum point, we can take the second derivative of V with respect to r:

d^2V/dr^2 = -6πr

At r=25 cm, this is negative, which indicates that we have a maximum point. Therefore, the dimensions calculated above do indeed maximize the volume of the cylinder.

For more questions like Volume click the link below:

https://brainly.com/question/1578538

#SPJ11

Answer:

y-axis

Step-by-step explanation:

points are (x,y)

since the y-coordinate does not change, but the x-coordinate does, it rotates around the y-axis.

reflection just means it rotates 180 degrees (out of the paper, not around)

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

To know more about the right circular cylinder, here

https://brainly.com/question/12762578

#SPJ4

Answer:

Exact form x = -21/2

decimal form x = -10.5

mixed number form x = -10 1/2

Step-by-step explanation:

Assuming you don't want decimal form or mixed form, then it will be -21/2

True. The 3px, 3py, and 3pz orbitals are similar in shape but differ in their orientation or direction.

The p orbitals are one type of orbital that corresponds to the angular momentum number l = 1. These p orbitals are designated as 3px, 3py, and 3pz to indicate their orientations along the x, y, and z axes, respectively.

The p orbitals have a  shape with a node at the nucleus. They consist of two lobes of electron density, one on either side of the nucleus, separated by a region of zero electron density. The lobes are oriented along the designated axes. The 3px orbital points along the x-axis, the 3py orbital points along the y-axis, and the 3pz orbital points along the z-axis. Although they have different orientations, their shapes and sizes are the same.

So, while the 3px, 3py, and 3pz orbitals differ in their orientation in space, they share the same overall shape and size.

Learn more about Shape:

brainly.com/question/24601545

#SPJ11

The base-4 representation of the binary number (11010010)_2 is 0322. When converting a binary number to base-4, we can group the binary digits into sets of two starting from the right and assign each group a base-4 digit.

Similarly, the base-4 representation of the hexadecimal number D is 23. In hexadecimal, D represents the decimal value 13, which is equivalent to the binary number 1101. By grouping the binary digits into sets of two from the right, we have 11 corresponding to 3 in base-4 and 01 corresponding to 2 in base-4. Therefore, the base-4 representation of (D)_16 is 23.

The base-4 representation of the hexadecimal number DDDDDDDD is 33333333. In hexadecimal, each digit represents a group of four binary digits. The hexadecimal digit D corresponds to the binary value 1101, so repeating D eight times gives us 11011101110111011101110111011101 in binary. By grouping the binary digits into sets of four, we can see that each set corresponds to the base-4 digit 3. Hence, the base-4 representation of (DDDDDDDD)_16 is 33333333.

The conversion is relatively easy in these cases because base-4 is a power of 2 (4 = 2^2). This allows us to directly map groups of binary digits to base-4 digits without converting the binary number into a decimal representation. By grouping the binary digits into sets of two or four, depending on whether we are converting from binary or hexadecimal, we can easily assign the corresponding base-4 digits.

Learn more about binary number here : brainly.com/question/28222245

#SPJ11

the answer to your question is 4 times 6, 4 times 3 + 4 times 3

have a nice day

Answer:

the answer to this math question is

4 times 6, 4 times 3 + 4 times 3

Step-by-step explanation:

Aleks Verfied

Answer: 2.82842712 or 2\(\sqrt{2}\)

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

5(x – 10) = 30 – 15x

Distribute

5x -50 = 30-15x

Add 15x to each side

5x+15x – 50 = 30 – 15x+15x

20x-50 = 30

Add 50 to each side

20x-50+50 = 30+50

20x = 80

Divide by 20

20x/20 = 80/20

x =4

Answer:

i think its A.

Step-by-step explanation:

To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

Learn more about rate here: brainly.com/question/25565101

#SPJ11

A. x and y are both within the same solar system.

7.2 light years= 455336 AU

Answer:

0.542

Step-by-step explanation:

divide the liter by 1000 and get your answer! have a great day

542 liters is approximately equal to 0.542.

Given that a quantity, 542 L we need to convert it into kL,

To convert liters (L) to kiloliters (kL), you need to divide the given value in liters by 1,000 since there are 1,000 liters in 1 kiloliter.

In this case, to convert 542 L to kL, you can use the following formula:

kL = L / 1000

Plugging in the given value:

kL = 542 L / 1000

Dividing 542 by 1000, you get:

kL ≈ 0.542 kL

Therefore, 542 liters is approximately equal to 0.542.

Learn more about Conversion Factor click;

https://brainly.com/question/30567263

#SPJ6

Let G be a group and let H be a subgroup of G of order k. We want to show that H is a normal subgroup of G.

Since H is a subgroup of G, it is closed under the group operation and contains the identity element. Therefore, H is a non-empty subset of G.

By Lagrange's Theorem, the order of any subgroup of G must divide the order of G. Since H has order k, which is a divisor of the order of G, there exists an integer m such that |G| = km.

Now consider the left cosets of H in G. By definition, a left coset of H in G is a set of the form gH = {gh : h ∈ H}, where g ∈ G. Since |H| = k, each left coset of H in G contains k elements.

Let x ∈ G be any element not in H. Then the left coset xH contains k elements that are all distinct from the elements of H, since if there were an element gh in both H and xH, then we would have x⁻¹(gh) = h ∈ H, contradicting the assumption that x is not in H.

Since |G| = km, there are m left cosets of H in G, namely H, xH, x²H, ..., xm⁻¹H. Since each coset has k elements, the total number of elements in all the cosets is km = |G|. Therefore, the union of all the left cosets of H in G is equal to G.

Now let g be any element of G and let h be any element of H. We want to show that ghg⁻¹ is also in H. Since the union of all the left cosets of H in G is G, there exists an element x ∈ G and an integer n such that g ∈ xnH. Then we have

ghg⁻¹ = (xnh)(x⁻¹g)(xnh)⁻¹ = xn(hx⁻¹gx)n⁻¹ ∈ xnHxn⁻¹ = xHx⁻¹

since H is a subgroup of G and hence is closed under the group operation. Therefore, ghg⁻¹ is in H if and only if x⁻¹gx is in H.

Since x⁻¹gx is in xnH = gH, and gH is a left coset of H in G, we have shown that for any g ∈ G, the element ghg⁻¹ is in the same left coset of H in G as g. This means that ghg⁻¹ must either be in H or in some other left coset of H in

To know more about statistics refer here:

brainly.com/question/29821285?#

SPJ11

Answer:

one hundred sixty million, twenty-nine thousand eight hundred thirty, thirty-five hundred thousandths

Step-by-step explanation:

Each of the numbers written in word form instead of standard form. Hope it helps!

(a) Linear differential equation of second order

(b) Linear differential equation of second order

(c) Linear differential equation of fourth order

(d) Non-linear differential equation of first order

(e) Non-linear differential equation of second order

(f) Linear differential equation of third order

(g) (a) and (d) are initial value problems

To learn more about calculus, visit :

https://brainly.com/question/22810844

#SPJ4

Answer:

Imposible!

Step-by-step explanation:

When it comes to passing a multiple choice math test without studying, it is important to understand that studying and preparation are key factors in achieving success. However, if you find yourself in a situation where you haven't had the opportunity to study, there are still some strategies you can employ to increase your chances of passing the test. Familiarize yourself with the format of multiple choice questions, read the questions carefully, eliminate obviously incorrect options, use the process of elimination, make educated guesses, and manage your time effectively. While these strategies may improve your chances of passing the test, it is important to note that studying and preparation are essential for long-term success in mathematics.

When it comes to passing a multiple choice math test without studying, it is important to understand that studying and preparation are key factors in achieving success. However, if you find yourself in a situation where you haven't had the opportunity to study, there are still some strategies you can employ to increase your chances of passing the test.

While these strategies may improve your chances of passing the test, it is important to note that studying and preparation are essential for long-term success in mathematics.

About pass multiple choice math test here:

https://brainly.com/question/30201357

#SPJ11

Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

Answer:

{1,2,3}

Step-by-step explanation:

The others will not show all the numbers from the set to make the inequality true

Answer:

1,2,3

Step-by-step explanation:

The 50th term is 290.

It is a sequence where there is a common difference between each consecutive term.

Example:

12, 14, 16, 18, 20 is an arithmetic sequence.

We have,

-4, 2, 8, 14,

This is an arithmetic sequence.

First term = a = - 4

Common difference.

d = 2 - (-4) = 6

d = 8 - 2 = 6

Now,

The nth term = a + (n -1)d

So,

n = 50

a = -4

d = 6

50th term.

= -4 + (50 - 1) 6

= - 4 + 49 x 6

= - 4 + 294

= 290

Thus,

The 50th term is 290.

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ9

The complete question:

What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?

The required cycle-time is approximately 57.6 seconds.

To find the required cycle time, we need to divide the total available time by the number of units to be produced.

Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds

Number of units to be produced: 1,000 units

Required cycle time: Total available time / Number of units

Cycle time = 57,600 seconds / 1,000 units

Cycle time ≈ 57.6 seconds

Therefore, the required cycle time is approximately 57.6 seconds.

Learn more about cycle-time from the given link

https://brainly.com/question/15356513

#SPJ11