An investor invested a total of $2,100 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If the investor’s total profit was $83, how much was invested in each mutual fund?

The amount invested in the mutual fund that earned 5% was $___.

The amount invested in the mutual fund that earned 3% was $___.

Answer:

680

Step-by-step explanation:

Answer:

680

Step-by-step explanation:

10 to the  2nd power is 10 times 10 which is 100.

Now, 6.8 times 100 is 680.

Hope this helps you!!

Answer:

B, D represent pairs of vertical angles.

___

Other pairs may be congruent, but they are not vertical angles. The lines that look parallel must be assumed to be NOT parallel, because they are not marked in the diagram as being parallel. Thus ∠8 ≠ ∠12, for example.

- sqdancefan

Answer:

i dont speak or type spanish

Step-by-step explanation:

Answer: Sorry, i don't speak spanish dude

Step-by-step explanation: Would you like to translate it for me?

Answer:

The cheapest way to purchase 9 liters of orange juice would be to buy 3 promotions of 2 1.5 liter bottles of drink at £ 5 each promotion, totaling £ 15.

Step-by-step explanation:

To obtain the cheapest way to buy 9 liters of orange juice, the cost per liter of each type of container must be determined:

500 ml bottle = £1.15 (£2.30 per liter)

1.5 l carton = £2.70 (£1.80 per liter)

2 cartons of 1.5 l = £5 (£1.66 per liter)

3.5 l carton = £5.75 (£1.64 per liter)

Thus, there is in principle a staggered way to buy the drink: 2 cartons of 3.5 liters, plus 1 carton of 1.5 liters, plus 1 bottle of 500 ml, which would add up to a total cost of £15.35 (5.75 x 2 + 2.70 + 1.15) .

Now, you could also take advantage of the promotion of 2 cartons of 1.5 l at £5, with which buying 3 of these promotions would acquire the 9 liters of drink (1.5 x 2 x 3) at £15 (3 x 5).

Thus, the cheapest way to purchase 9 liters of orange juice would be to buy 3 promotions of 2 1.5 liter bottles of drink at £ 5 each promotion, totaling £ 15.

Answer/Step-by-step explanation:

The two triangles we have in the diagram shar the same vertex. They are both similar triangles. Therefore, their side lengths would be proportional.

This means:

[tex] \frac{9.8}{4.3} = \frac{r}{5.1} = \frac{n}{2.7} [/tex]

Solve for variable r and n respectively.

Thus:

[tex] \frac{9.8}{4.3} = \frac{r}{5.1} [/tex]

Multiply both besides by 5.1

[tex] \frac{9.8}{4.3} \times 5.1 = \frac{r}{5.1} \times 5.1 [/tex]

[tex] \frac{9.8 \times 5.1}{4.3} = r [/tex]

11.6 = r (nearest tenth)

Also,

[tex] \frac{9.8}{4.3} = \frac{n}{2.7} [/tex]

Multiply both besides by 2.7

[tex] \frac{9.8}{4.3} \times 2.7 = \frac{n}{5.1} \times 2.7 [/tex]

[tex] \frac{9.8 \times 2.7}{4.3} = r [/tex]

6.2 = n (nearest tenth)

Answer:

Step-by-step explanation:

33.366/6.7=  4.98

Answer:

1/16

Step-by-step explanation:

The probability of getting heads with 1 coin toss is 1/2.

For 4 tosses, the probability is 1/2 * 1/2 * 1/2 * 1/2 = 1/16

Answer:Its B

Step-by-step explanation:

Bc I just got it right

ARM for which interest will stay fixed for 8 years and then be adjusted every year after that = 8/1 ARM

The correct option is (B).

The term adjustable-rate mortgage (ARM) refers to a home loan with a variable interest rate. With an ARM, the initial interest rate is fixed for a period of time. After that, the interest rate applied on the outstanding balance resets periodically, at yearly or even monthly intervals.

Given statement

ARM for which Interest rate stay fixed for 8 years and then be adjusted every year after that.

Above information is typically expressed in two numbers. The first number indicates the length of time that the fixed rate is applied to the loan, while the second refers to the duration or adjustment frequency of the variable rate.

By the above method ARM for Interest rate stay fixed for 8 years and then adjusted every year after that can be expressed as 8/1 ARM.

Hence, for 8/1 ARM, interest rate will stay fixed for 8 years and then

be adjusted every year after that.

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Answer:

a

   [tex]P(X = 5) = 0.2423 [/tex]

b

    [tex]P( X \ge  6 )=  0.4516 [/tex]

c

   [tex]P( X <  4 )=  0.12694[/tex]

Step-by-step explanation:

From the question we are told that

   The population proportion is   p = 0.53

    The sample size is  n = 10

Generally the distribution of the confidence of US adults in newspapers follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

and the probability distribution function for binomial  distribution is  

      [tex]P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators        

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is exactly​ five is mathematically represented as

     [tex]P(X = 5) =  ^{10}C_5 *  0.53^5 *  (1- 0.53)^{10-5}[/tex]

=>  [tex]P(X = 5) =  252 * 0.04182 *  0.023[/tex]

=>  [tex]P(X = 5) = 0.2423 [/tex]

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is  at least​ six is mathematically represented as

  [tex]P( X \ge 6 )= P( X = 6) + P( X = 7) + P( X = 8) + P( X = 9) + P( X = 10)[/tex]

=> [tex]P( X \ge  6 )=  [^{10}C_6 *  [0.53]^6 *  (1- 0.53)^{10-6}] +  [^{10}C_7 *  [0.53]^7 *  (1- 0.53)^{10-7}] +  [^{10}C_8 *  [0.53]^8 *  (1- 0.53)^{10-8}] +  [^{10}C_9 *  [0.53]^9 *  (1- 0.53)^{10-9}] + [^{10}C_{10} *  [0.53]^{10} *  (1- 0.53)^{10-10}][/tex]

=> [tex]P( X \ge  6 )=  [0.227] +  [0.1464] +  [0.0619] +  [0.0155] + [0.00082][/tex]

=> [tex]P( X \ge  6 )=  0.4516 [/tex]

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is  less than four is mathematically represented as

    [tex]P( X < 4 )= P( X = 3) + P( X = 2) + P( X = 1) + P( X = 0)[/tex]

=>  [tex]P( X <  4 )=  [^{10}C_3 *  0.53^3 *  (1- 0.53)^{10-3}] +  [^{10}C_2 *  0.53^2 *  (1- 0.53)^{10-2}] +  [^{10}C_1 *  0.53^1 *  (1- 0.53)^{10-1}] +  [^{10}C_0 *  0.53^0 *  (1- 0.53)^{10-0}] [/tex]

=>  [tex]P( X <  4 )=  0.09051  +  0.03 +  0.0059 +  0.000526[/tex]

=>  [tex]P( X <  4 )=  0.12694[/tex]

Answer:

If 3 letters are picked from the word 'PROBABILITY', the chances of it being P is 33.33%.

Hope this helps and if you could mark me as brainliest. Thanks!

The answer is 43 because when you multiply 6x6 you get 36 and if you add 6 more you get 42 which is one less that 43

Answer:

a. The following will be needed to make 6 dozen cakes:

Number of grams of butter needed = 600g

Number of grams of sugar needed = 2,000g

Number of grams of currants needed = 400g

b. The number whole that cakes could be made with 1kg of butter is still 18 whole cakes.

Step-by-step explanation:

a. how many of each ingredient will be needed to make 6 dozen cakes

This can be calculated as follows:

One dozen = 12

Number of small cakes in 6 dozen cakes = 6 * 12 = 72 small cakes

Number of 18 small cakes that can be obtained from 72 small cakes = 72 / 18 = 4

Therefore, we multiply each ingredient by 4 to obtain the number oof each ingredient that will be needed to make 6 dozen cakes as follows:

Number of grams of butter needed = 150 * 4 = 600g

Number of grams of sugar needed = 500 * 4 = 2,000g

Number of grams of currants needed = 100 * 4 = 400g

b. how many whole cakes could be made with 1kg of butter

Ordinary in terms of measurement, we have:

1kg = 1,000g

Since it is not indicated in the question that additional grams of other ingredients are made available, only 150g butter will be used out of the 1,000g butter made available together with already available 500g sugar and 100g currants to make just 18 cakes. This implies that no additional whole cakes will be made to add to the current 18 small cakes that is being made. Additional whole cakes would only be made when additional grants of sugar and currants are made available.

Therefore, the number whole that cakes could be made with 1kg of butter is still 18 small cakes.

Answer:

y = 2

Step-by-step explanation:

For the equation x - y = -1, if x = 1,

then we would plug that in to solve for the y value

1 - y = -1

Subtract 1 from both sides to find y

-y = - 2

Divide by -1 to find y

y = 2.

To double check our answer we would plug in our x-value and y-value into the equation

1 - 2 = -1

This is true, so our answer is y = 2

Answer:

y = 2

Step-by-step explanation:

x - y = -1

1 - y = -1

1 + 1 - y = 0

2 - y = 0

2 = y

y = 2

Answer: z>0.6

Step-by-step explanation:

You isolate the variable by dividing each side by factors that don’t contain the variable.

The answer is verified it came from Math-way .

Answer:

z≥0.6

Step-by-step explanation:

Answer:

You may want to check your question but I've solved various circumstances. Please mark as brainliest :-)

Step-by-step explanation:

[tex]v = 2 - 5t [/tex]

Although, I think you're meant to find time(t) making velocity (v) =0. So,

[tex]0 = 2 - 5t \\ - 2 = - 5t \\ t = - 2 \div - 5[/tex]

If time is 0, then,

[tex]v = 2 - 0 \\ v = 2[/tex]

Answer:

478miles

Step-by-step explanation:

32=1gallons 32×15 = 510miles

15g

510- 32= 478miles

Answer:

have

Step-by-step explanation:

Have is used alongside plural nouns , And has is used alongside singular nouns. So books and supplies are plural so you use have

Answer:

21x^4 + 8x + 7

Step-by-step explanation:

This is the answer because:

1) Simplify each term and multiply like terms and multiply them because in order to find the area we have to multiply the height and width.

2) Since we have to multiply like terms, 7x^2 and 3x^2 are the only like terms. Therefore, we multiply 7x^2 * 3x^2 = 21x^4.

3) The rest of the numbers are not like terms.

4) Therefore, the answer is 21x^4 + 8x + 7

Hope this helps!

Answer:

34.12-9.8=24.32

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

First you have to do this step to find your slope: y2-y1/x2-x1

So your first point is (0,-4) (3,-3)

I got 1/3

You can also do rise over run as well

Answer:

88

Step-by-step explanation:

Hope this helps

plzz mark brainliest

Answer:

This question doesn't really make sense...

Step-by-step explanation:

Please try to correct it.

Answer:

9 is the answer

Step-by-step explanation:

1. 31 = 9/3+6 <------- This is the original equation.

2. 31 = 3+6    <------- Simplify the fraction.

3. 31 = 9        <-------- This is the final answer.

Hope this helps! I did the best I could. :)

Answer:

35

Step-by-step explanation:

Answer:

8.4 hours

Step-by-step explanation:

Given that:

Speed of asteroid = 55000 miles/hr

Distance traveled by asteroid = 4.62 [tex]\times[/tex] [tex]10^5[/tex] miles

We are required to find here how many hours the asteroid will take to travel the given distance with the given speed.

Formula for speed can be given as following:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

OR, the formula for time in terms of speed and distance can be given as following:

[tex]Time= \dfrac{Distance}{Speed}[/tex]

Putting the given values in the formula to find the Time:

[tex]Time= \dfrac{4.62\times 10^5}{55000}\\\Rightarrow \bold{Time = 8.4\ hours}[/tex]

Answer:

A

Step-by-step explanation:

b<3

The solution graph of the given inequality is graph 1.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Given that, an inequality -3b - 15 > - 24, we need to graph its solution,

-3b - 15 > - 24

Add 15 both sides,

-3b-15+15 > -24+15

-3b > -9

b < 3

Since, the sign does not include equal to (> or <), the circle will be unfilled.

And the solution will be all the number less than 3,

Therefore, the graph with the unfilled circle, having the arrow with head facing left will be the solution.

Hence, the solution graph of the given inequality is graph 1.

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Answer:

Ah yes that is a reflection because all of the points were reflected on the y axis

Your question: "Which equation represents the polar form of x – y = 0?"

Answer:

b. Theta = pi/4

We want to write an equation that represents the polar form of:

x - y = 0.

We will see that the correct option is b, the polar form is given by:

θ = pi*/4

First, polar form is a way to write equations using radius and angle as variables, instead of the known x and y that we usually use.

To change the variables we have the general rule:

R = √(x^2 + y^2)

θ = Atan(y/x)

So here we have:

x - y = 0.

Then we can write this as:

x = y.

Then the angle is given by:

θ = Atan(y/x) = Atan(x/x) = Atan(1) = 45°

Writing this in radians we get:

45° = 45°*(pi/180°) = pi*/4

Then we have:

θ = pi*/4

Then the equation that represents the polar form is:

θ = pi*/4

From this, we can see that the correct option is b.

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