Dave ordered dinner for a party of 10 people. Three people ordered the $4.75 chicken dinner, two people ordered the $4.95 fish dinner, and five had the beef dinner at a cost of $6.75 each. what was the average cost of each dinner at Dave's party?

Answer:

The correct answer is B. 87°

Step-by-step explanation:

Let's recall that the interior angles of a triangle add up to 180°,

therefore, we have:

∠x + 28 + 65 = 180

∠x = 180 - 65 -28

∠x = 180 - 93

∠x = 87°

The correct answer is B. 87°

Answer:

[tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex]  =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]

[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex]   =   [tex]{{$log_{nb} \left(x\right)$}}[/tex]

Step-by-step explanation:

i) [tex]$\log_{nb} x[/tex]   =  [tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex]  =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]

ii) therefore simplifying i) we get

    [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex]   =   [tex]{{$log_{nb} \left(x\right)$}}[/tex]

iii) Hence the equation is proved.

Answer:

25%

Step-by-step explanation:

50% chance for spin one to be gray and 50% chance for spin two to be blue. Put them together for that order and you get 25%.

Answer:

Let's Take 8 sections and in which 6 are grey and 2 are blue.

The probability that the first spin lands on blue = 2/8 = ¼

The probability that the second spin lands on gray = 6/8 = ¾

 The probability that the first spin lands on blue and the second spin lands on gray is

(¼)(¾) = 3/16

These events are independent, so you can just multiply the probabilities

Answer:

4

Step-by-step explanation:

its a parabola that opens upward, the zeros are x=4 and x=3

By setting up a system of equations from the given scenarios, we find that the cost of a burrito platter is $32 and the cost of a taco platter is $26.

To solve Carmen's problem about the cost of burrito and taco platters, we need to set up a system of equations based on the information given.

We know she spent $58 on one burrito platter and one taco platter and $90 on two burrito platters and one taco platter.

Let's denote the cost of a burrito platter as B and the cost of a taco platter as T.

Step 1: Establish the Equations

The first scenario gives us the equation: B + T = 58.
The second scenario gives us the equation: 2B + T = 90.

Step 2: Solve the Equations

From the first equation, we can express T in terms of B: T = 58 - B.

Therefore, the cost of a burrito platter is $32 and the cost of a taco platter is $26.

Answer:

Step-by-step explanation:

Least common number for 9 and 12 is 36

36/9=4

36/12=3

4 packs of hot dogs and 3 packs of buns

Answer:

y = 10

Step-by-step explanation:

The question is a simple equation and ought to be 3y/5 = 6 ( in stead of 3/5y=6)

Multiply through by the lowest common multiple (LCM) of denominator (which equals 5)

5 × 3y/5 = 6 × 5

3y = 30

Divide through by 3

3y/3 = 30/ 3

y = 10

Therefore, y = 10

Check

3y/5 = 6

y = 10

3(10)/5 = 6

30/5 = 6

6 = 6

The answer for P(A∪B) is 40/45 (or) 8/9.

Step-by-step explanation:

Given,

The number of students that play only stringed instruments (A) = 35 students.

The number of students that play only brass instruments (B) = 10 students.

The number of students that play both of the instruments = 5 students.

The number of students that play none of the instruments = 5 students.

Probability = Number of required events / Total events

To find the total number of students,

TOTAL = A + B - both + neither.

TOTAL = 35 + 10 - 5 + 5 = 45 students.

P(A∪B) = P(A) + P(B) - P(A∩B)

Probability of A, P(A) = 35 students / 45 students = 35/45

Probability of B, P(B) = 10 students / 45 students = 10/45

Probability of A∩B (both), P(A∩B) = 5 students / 45 students = 5/45

P(A∪B) = (35/45) + (10/45) - (5/45)

             = 40/45

P(A∪B)  = 8/9

Answer:

2300-x(250) is the best i could think of hope it helps

Step-by-step explanation:

We need to represent the value of a TV whose value decreases yearly.

The required equation is [tex]y=2300-250x[/tex]

The cost of the TV set is $2300.

The decrease in value is $250 per year.

Let [tex]x[/tex] be the number of years that has passed after buying the TV

and [tex]y[/tex] be the cost of TV after [tex]x[/tex] years have passed.

The linear equation that represents the situation is [tex]y=2300-250x[/tex]

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the answer to your question is 7

Answer:

4x + 3

Step-by-step explanation:

(-6 + 7) - ( -4x - 2)

1 - ( -4x -2 )

distribute the negative sign to the parenthesis

( remember a negative plus a negative equals a positive )

1 + (4x + 2)

Answer: 4x + 3

Marissa walked her dog 1/10 mile on saturday and 55/100 mile on sunday. how far did she walk her dog in all?​

Marissa walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday

Given that, Marissa walked her dog

From given information,

[tex]\text{Miles walked on saturday } = \frac{1}{10} \text{ mile }\\\\\text{Miles walked on sunday } = \frac{55}{100} \text{ mile }[/tex]

We have to find the distance walked in all

[tex]\text{Total distance } = \text{Miles walked on saturday + Miles walked on sunday }[/tex]

Substituting the values we get,

[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]

Make the denominators same for easier calculations by taking L.C.M of 10 and 100

Prime factors of 10 = 2 x 2 x 5

Prime factors of 100 = 2 x 2 x 5 x 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 5, 5

Multiply these factors together to find the LCM

LCM = 2 x 2 x 5 x 5 = 100

[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]

[tex]\text{Total distance } = \frac{1 \times 10}{10 \times 10} + \frac{55}{100}\\\\\text{Total distance } = \frac{10}{100} + \frac{55}{100}\\\\\text{Total distance } = \frac{10+55}{100} = \frac{65}{100}[/tex]

Thus she walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday

Answer:

The answer is B ⅚ because there's only one out of 6 chance that the spinner will land on 6.

Answer:

[tex]x = \$187n[/tex]

Step-by-step explanation:

let x be the total cost in dollars for two days for the n members

Given:

The first day the members paid $70 for transportation plus $15 per ticket to the planetarium.

The second day they paid $90 for transportation plus $12 per ticket to the geology museum.

We need to write an an expression to represent the total cost in dollars for two days for the n members of the club.

Solution:

First day each member pay $70 for transportation and $15 for ticket,

[tex]Cost\ per\ member\ for\ the\ first\ day = transportation\ cost+ticket\ cost[/tex]

[tex]Cost\ per\ member\ for\ the\ first\ day = 70+15[/tex]

[tex]Cost\ per\ member\ for\ the\ first\ day = \$85[/tex]

Therefore, cost for n members for the first day.

[tex]Cost\ for\ n\ member\ for\ the\ first\ day = \$85n[/tex]

Similarly for the second day each member pay $90 for transportation and $12 for ticket,

[tex]Cost\ per\ member\ for\ the\ second\ day = transportation\ cost+ticket\ cost[/tex]

[tex]Cost\ per\ member\ for\ the\ second\ day = 90+12[/tex]

[tex]Cost\ per\ member\ for\ the\ second\ day = \$102[/tex]

Therefore, .

[tex]Cost\ for\ n\ member\ for\ the\ second\ day = \$102n[/tex]

Now, we write an expression to represent the total cost in dollars for two days for the n members of the club, so cost for n members for two days is equal to sum of the two days expenses for n members.

[tex]Cost\ for\ n\ member\ for\ the\ two\ day = \$85 + \$102n[/tex]

[tex]x = \$85n + \$102n[/tex]

[tex]x = \$187n[/tex]

Therefore, total cost for two days for the n members [tex]x = \$187n[/tex]

Answer:15pq

Step-by-step explanation:

The correct expression is 15pq.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given:

(3p)(5q).

=3p * 5q

=15 pq

Hence, the simplified expression is 15 pq.

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Answer:

x intercept is 15 and y intercept is -3.75

Step-by-step explanation:

The first thing is to form equation with the given tow point using the formula

y-y1/x - x1 = y2 - y1/ x2 - x1

y + 5/x + 5 = -2 + 5/7 + 5

y + 5/x + 5 = 3/ 12

3x + 15 = 12y + 60

12y - 3x = -45

On x intercept y = 0

x = 15

On y intercept x = 0

y = -3.75

The correct answer is B) [tex]$1606.42[/tex]. The balance after Anna writes check  is

 [tex]$1606.42[/tex].

To solve this problem, we need to follow the transactions in Anna's checking account to determine the balance after check #1620 is written. Let's assume that the initial balance before any transactions is $0.00.

 Let's check each option:

A) [tex]$1536.24[/tex][tex]- $1452.77 = $83.47[/tex] (This cannot be the correct balance after check #1620 because it does not match the balance after check #1612.

B)[tex]$1606.42 - $1452.77 = $153.65[/tex] (This is the amount spent on groceries, indicating that the balance after check #1612 is correct and no additional funds were withdrawn by check #1620.)

 C)[tex]$1734.81[/tex][tex]- $1452.77 = $282.04[/tex] (This would mean an additional $282.04 was withdrawn after the groceries purchase, which is not possible since we are looking for the balance after one check, #1620.)

 D) [tex]$1760.61[/tex][tex]- $1452.77 = $307.84[/tex] (This would also mean an additional amount was withdrawn, which is not possible for the same reason as option C.) Therefore, the only logical balance that matches our calculations after check #1620 is option B) $1606.42, which implies that check #1620 did not change the balance from what it was after check #1612. This means that check #1620 was for the same amount as the groceries purchase ($153.65), which brought the balance back to $1606.42 after the groceries were bought

Answer:

Sorry I can't read it :(

Answer:

0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)

0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)

Step-by-step explanation:

Let's remember that multiplying decimals is the same as multiplying whole numbers except that you have to put the decimal point in the answer. When you multiply decimals, the decimal point is placed on the product so that the number of decimal places in the product is the sum of the decimal positions of the factors.

Example:

214 * 32 = 6,848

0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)

7 * 11 = 77

0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)

Step-by-step explanation:

To find fg(x), you first open up the g.

This will make f(6x+5). How you substitute 6x + 5 for the x in the f.

This means you get 2(6x+5)+4

Which equals 12x+14

Answer:

-10

Step-by-step explanation:

2-12 =

-12+2 = -10

Answer:

My best guess is 384 ft

Step-by-step explanation:

Tangent 38° = opposite side / adjacent side

Tangent 38° = 300 ft / x ft

The value of x from the equation is 383.98 ft. Thus, the engineer is 383.98 ft.

Rounding it up gives us 384 ft.

Answer:

384 ft.

Step-by-step explanation:

We know the opposite side of the triangle and we need the adjacent side.

So tan 38 = opposite / adjacent

= 300 / x

x = 300 tan 38

x = 383.98 feet.

Answer:

-2 degrees celcius

Step-by-step explanation:

-6/3

Answer:

Each day, the temperature rises plus -6 Celsius

The rate change of interval for the given table is Constant , so the function a linear function.

Step-by-step explanation:

A linear function is defined as a function which yields a line in a graph and the rate of change(constant) is called as slope.

Since the rate is constant, then function will result in a straight line.

From the given table the slope m=1 and it changes constantly.

The linear equation formula is y=mx+c.

where m is the slope and c is the y-intercept.

The linear equation for the given table is y=x+1.

∴ The rate change of interval for the given table is Constant , so the function a linear function.

If the graph for a function has any shapes other than a straight line then it doesn't have a constant slope and it will be a non-linear function.

Answer:

[tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]

Step-by-step explanation:

Given hours is from 4:56 P.M. to 5:32 P.M.

Now, finding the part of an hour elapases.

We know the starting time is 4 minutes to 5:00 P.M and end time is 32 minutes past 5 P.M.

∴ Total times elapses= [tex]4\ minutes + 32\ minutes= 36\ minutes[/tex]

Hence, 36 minutes elapses out of an hour.

Remember; 1 hours= 60 minutes

Next, finding the fraction of an hour elapses.

[tex]Part\ of\ an\ hour\ elapses= \frac{36}{60}[/tex]

∴ [tex]Part\ of\ an\ hour\ elapses= \frac{3}{5} \ hour[/tex]

Hence, [tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]  from 4:56 P.M. to 5:32 P.M.

Answer:

30 miles/1 hour is the unit rate.

Step-by-step explanation:

This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.

[tex]F(x)+G(x)=3x^2+2x-2.[/tex]

Solution:

Given data: [tex]F(x)=3x^2+1[/tex] and [tex]G(x)=2x-3[/tex]

To find F(x) + G(x):

Adding two functions which gives another function.

Substitute F(x) and G(x), we get

[tex]F(x)+G(x)=(3x^2+1)+(2x-3)[/tex]

                    [tex]=3x^2+1+2x-3[/tex]

                    [tex]=3x^2+2x-3+1[/tex]

                    [tex]=3x^2+2x-2[/tex]

[tex]F(x)+G(x)=3x^2+2x-2[/tex]

Hence, [tex]F(x)+G(x)=3x^2+2x-2.[/tex]

Answer: C

Step-by-step explanation: simply apply the distributive property to each half of the expression to be left with terms that can be combined.

(8x + 16y)/2 = 4x + 8y

4(x - y) = 4x - 4y

(4x + 8y) + (4x - 4y) = 4x + 4x + 8y - 4y

= 8x + 4y => C

Answer:

[tex]\frac{8x+16y}{2}+4(x-y)=\frac{2*4x+2*8y}{2}+4*x-4*y\\\\=\frac{2*(4x+8y)}{2}+4x-4y\\\\=4x+8y+4x-4y=8x+4y[/tex]

Step-by-step explanation:

Answer:

x - 5.19 or x = -2.67 is the correct answer.

Step-by-step explanation:

Here, the given quadratic equation is:  [tex]2x^2- 5x-28=0[/tex]

To solve it by : Completing The Square

Step : 1  Make the coefficient of leading variable x² as  1.

Divide whole equation by 2,we get:

[tex]x^2- \frac{5}{2} x-14=0\\\implies x^2- \frac{5}{2} x = 14[/tex]

Step 2: Find the coefficient of x in the equation and DIVIDE it by 2 to HALF THE VALUE

Here, the coefficient of x = (-5/2)

Dividing ot by 2, we get the value =  (-5/4)

Step 3: ADD THE SQUARE of the found value on BOTH sides.

And USE: [tex](a - b)^2 = a^2 + b^2 - 2ab[/tex]

[tex]x^2- \frac{5}{2} x = 14 \implies x^2- \frac{5}{2} x + (\frac{5}{4} )^2= 14 + (\frac{5}{4} )^2\\\implies (x -\frac{5}{4})^2 = 14 + \frac{25}{16} = \frac{224 + 25}{16} = \frac{249}{16} \\\implies (x -\frac{5}{4})^2 = \frac{249}{16} = (\frac{15.7}{4})^2\\ \implies (x -\frac{5}{4})^2 = (\frac{15.7}{4})^2[/tex]

Step 4: TAKE ROOT ON BOTH SIDES, we get:

[tex](x -\frac{5}{4})^2 = (\frac{15.7}{4})^2\\\implies (x -\frac{5}{4}) = \pm (\frac{15.7}{4})\\\implies x = (\frac{15.7}{4}) +(\frac{5}{4}) = 5.19\\or, x = - (\frac{15.7}{4}) +(\frac{5}{4}) = -2.67\\[/tex]

So, either x - 5.19 or x = -2.67

Answer:

x = 6

Step-by-step explanation:

Given ∠ 1 = ∠ 2 then the segment is an angle bisector and the ratios of sides to base are equal, that is

[tex]\frac{3}{x-4}[/tex] = [tex]\frac{x}{4}[/tex] ( cross-  multiply )

x(x - 4) = 12 ← distribute left side

x² - 4x = 12 ( subtract 12 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

However, x > 0 , thus x = 6