a bank loaned out $19000, part of it at the rate of 7% per year and the rest at 15% per year. if the interest received in one year totaled $2000, how much was loaned at 7%? How much of the $19000 did the bank loan out at 7%?

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x +2}{4}=8}[/tex]

[tex]\large\textsf{MULTIPLY 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{x +2}{4}\times4=8\times4}[/tex]

[tex]\large\textsf{CANCEL out: 4}\times\large\textsf{4.}[/tex]

[tex]\large\textsf{KEEP: 8}\times\large\textsf{4 because it helps you solve for x}[/tex]

[tex]\mathsf{8\times4=\bf 32}[/tex]

[tex]\large\text{New equation: \textsf{x + 32 = \bf 32}}[/tex]

[tex]\large\textsf{x + 2 = 32}[/tex]

[tex]\large\textsf{SUBTRACT 2 to BOTH SIDES}[/tex]

[tex]\mathsf{x +2-2=32-2}[/tex]

[tex]\large\textsf{CANCEL out: 2}-\large\textsf{2 because that gives you 0}[/tex]

[tex]\large\textsf{KEEP: 32}-\large\textsf{2 because that helps you solve for x}[/tex]

[tex]\large\textsf{New EQUATION: \mathsf{x = 32 - 2}}[/tex]

[tex]\mathsf{x = 32 - 2}[/tex]

[tex]\large\textsf{Simplify above and you have your result to this equation}[/tex]

[tex]\mathsf{32-2=\bf 30}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x =30}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

5.831

Step-by-step explanation:

Distance between both given points=Lenght=5.831

Answer:

28.83

Step-by-step explanation:

Answer:

x=7cm.

Step-by-step explanation:

A=1/2(a+b)h.

63=1/2(6+12)x.

63=1/2(18)x.

63=9×x.

63/9=9×x/9.

7cm=x.

x=7cm.

Answer:

0.6808 = 68.08% probability that it will rain on at least 3 of the next 5 days.

0.9898 = 98.98% probability it will rain on at least 1 of the next 5 days.

0.84 = 84% probability it will rain on at least 1 of the next 2 days.

Step-by-step explanation:

For each day, there are only two possible outcomes. Either it rains, or it does not. The probability of raining on a day is independent of any other day. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

There is a 60% probability of rain each of the next 5 days.

This means that [tex]p = 0.6, n = 5[/tex]

Probability it will rain on at least 3 of the next 5 days:

This is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

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

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102[/tex]

[tex]P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768[/tex]

[tex]P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304[/tex]

So

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0120 + 0.0768 + 0.2304 = 0.3192[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.3192 = 0.6808[/tex]

0.6808 = 68.08% probability that it will rain on at least 3 of the next 5 days.

Probability it will rain on at least 1 of the next 5 days:

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

From the above item, we have that [tex]P(X = 0) = 0.0102[/tex]. So

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0102 = 0.9898[/tex]

0.9898 = 98.98% probability it will rain on at least 1 of the next 5 days.

Probability it will rain on at least 1 of the next 2 days:

Two days means that [tex]n = 2[/tex].

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.6)^{0}.(0.4)^{2} = 0.16[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.16 = 0.84[/tex]

0.84 = 84% probability it will rain on at least 1 of the next 2 days.

The answer is b          

saddsadsadas

Answer:

B

Step-by-step explanation:

Cause he added 24.76 more pounds to the 3.6 pounds. So you can take 24+3=27 and you might think C, but 0.76+0.6 that equals more than 1, so 27+1=28, and B has 28 as its answer, so its B

B

Answer:

The right answer is :

(a) 23,200

(b) 24,514

(c) 22,926

Step-by-step explanation:

According to the question,

[tex]P_1 = 12000[/tex]

[tex]P_2 = 20000[/tex]

[tex]P_{sat}=80000[/tex]

(a)

We know that the arithmetic growth formula will be:

⇒ [tex]P=Pi+K\times t[/tex]...(1)

here,

⇒ [tex]K=\frac{P_2-P_1}{\Delta t}[/tex]

        [tex]=\frac{20000-12000}{25}[/tex]

        [tex]=\frac{80000}{25}[/tex]

        [tex]=320[/tex]

On putting the values in equation (1), we get

⇒ [tex]P_{2020}=20000+320\times 10[/tex]

             [tex]=23,200[/tex]

(b)

The geometric growth formula will be:

⇒ [tex]P=ln(Pi)+K\times t[/tex]

here,

⇒ [tex]K=\frac{lnP_2-lnP_1}{\Delta t}[/tex]

         [tex]=\frac{ln(20000)-ln(12000)}{25}[/tex]

By putting the values of general log, we get

hence,

⇒ [tex]P_f=ln(20000)+0.0204\times 10[/tex]

         [tex]=10.107[/tex]

[tex]P_{2020}=e^{10.107}[/tex]

          [tex]=24,514[/tex]

(c)

⇒ [tex]P_f=P_{sat}-(P_{sat}-P_i)e^{-K\times t}[/tex]

or,

⇒ [tex]K=-\frac{1}{\Delta t}ln(\frac{P_{sat}-P_2}{P_{sat}-P_1} )[/tex]

from here, we get

        [tex]=0.005[/tex]

hence,

⇒ [tex]P_{2020}=80000-(80000-20000)e^{-0.005\times 10}[/tex]

             [tex]=80000-(60000)e^{-0.005\times 10}[/tex]

             [tex]=22,926[/tex]

Answer:

Step-by-step explanation:

A linear equation can be written in the form

y = mx+b.

y = x² is not linear.

Answer:

Randomly selecting a six of diamonds - 1 / 52

Randomly selecting a 7, 8, 9 or 10 - 4 / 13

Step-by-step explanation:

There is only 1 six of diamonds in a standard deck of cards. There are 52 cards in a deck, thus the probability of pulling a six of diamonds is 1 in 52.

There are 4 of each card in a deck. so they are 4 7's, 4 8's. 4 9's and 4 10's. And there are a total of 52 cards in a deck. So the probability of pulling a 7,8,9 or 10 are 4 + 4 + 4 + 4 in 52

4 + 4 + 4 + 4 = 16

16 / 52 simplified is 4 / 13 Therefore the is a 4 in 13 chance of pulling a 7 8 9 or 10

The other ones are correct

A. Right triangles.

B. Height of 16cm with bases 20cm

C. 320

D.?

Answer:

A. 130°

Step-by-step explanation:

Answer:130

Step-by-step explanation:

I just finished the quiz :)

Answer:

$258.48

Step-by-step explanation:

Answer:

Kilo —> 1×10³ grams

nano —> 0.000000001 meters

micro —> mean " one millionth"

centi —> 0.01 liters

Answer:

120 brainliest?

Step-by-step explanation:

Answer:

150°

Step-by-step explanation:

An obtuse angle is always 120°. You have to add 30 to it in order to get your final answer.

Answer:

1. 21%   2.  70%

Step-by-step explanation:

1. 21 out of 100 are filled in

2. 7/10 are filled in

Answer: One

Step-by-step explanation: Recall that intersecting lines have one solution and therefore the system is consistent. Because the lines are not the same, the equations are independent.

Answer:

b and c

Step-by-step explanation:

x=5 so its basically 1+5=6 and 7-5=2

Answer:

150

Step-by-step explanation:

Remark

The exterior angle = the sum of the two given interior angles. The first job is to solve for x and then use that to find the exterior angle.

Equation

83 + 6x + 7 = 15x              

Solution

Combine like terms

90 + 6x = 15x        Subtract 6x from both sides.

        6x     6x

90 = 9x                 Divide both sides by 9

90/9 = 9x/9

x = 10

Now the exterior angle = 15x

Exterior angle = 15*10

Exterior angle = 150

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

since 3 is outside the parenthesis (n + 2) you multiply the 3 by the n and the 2 and

3n + 6

next subtract the 6 and add the 6 to the other side

3n - 6 = 6

3n = 6

n = 2

Answer:

1. 2,555

2. 23.25

Step-by-step explanation:

1. 5+10+20+...

S9 = 5(2^9-1)/(2-1)

= 5(511) = 2,555

2. 12+6+3+1.5+0.75 = 23.25

14.80 is the answer

1 1

13.95

95

80

1 4

To find the total cost you need to multiply the hourly rate by the number of hours they work and add the fixed fee.

C = 17h + 15

Answer:

Just hoping this helps.

Answer:

a = 7

b = 7[tex]\sqrt{2}[/tex]

Step-by-step explanation:

in a 45-45-90° triangle, the length of legs to hypotenuse is 1 : [tex]\sqrt{2}[/tex]