8. A goldsmith has 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold. How
much pure gold must be added to this alloy to obtain an alloy that is 90% pure gold?
The amount of pure gold that should be added is
(Type an integer or a decimal.)
grams.

Answer:

State A was the 12th state to enter the Union. State B was the 11th state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)} [/tex]

[tex]x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)} [/tex]

[tex]x = \frac{-1 \pm 23}{2} [/tex]

[tex]x_1 = \frac{-1 + 23}{2} [/tex]

[tex]x_1 = 11 [/tex]

[tex]x_2 = \frac{-1 - 23}{2} [/tex]

[tex]x_2 = -12[/tex]

The negative solution has no sense in the context of our problem, then the solution is x = 11.

Answer:

O {-8, 8}

Step-by-step explanation:

[tex]-|x| = -8\\\\\frac{-|x|=-8}{-1}\\\\|x|=8\\\\\text{Apply rule: If } |u|=a, a > 0, \text {then } u=a \text { or } u=-a\\\\\boxed {x = -8, x = 8}[/tex]

Answer: 3^2 + 8×4

= 41

3^2=9, 8 ×4=32 9 +32=41

Step-by-step explanation:

You can use the carat ^ to indicate an exponent. On a standard keyboard it's above the 6. (shift +6).

I have the same problem on my phone keyboard.

In Brainly, you might be able to use the formula options.

Answer:

41

Step-by-step explanation:

3^2 + 8(4)

Multiply 8 by 4

3^2 + 32

Square 3

9 + 32

Add 9 and 32 to get the answer

41

hope this helps!

Answer: A, C, and E

Step-by-step explanation:

Hi, to answer this question we have to analyze the function given:

C(b) = 2.75b + 10

Where:

So:

A. The number of books purchased is the independent variable. TRUE  

B. The input is the yearly cost. (FALSE, the input is the number of books )

C. The total yearly cost depends on the number of books purchased. TRUE

D. The number of books purchased is determined by the yearly cost. FALSE , the yearly cost is determined by the number  

of books.

E. The output is the yearly cost.TRUE

Answer:

A)The number of books purchased is the independent variable.

C)The total yearly cost depends on the number of books purchased.

E)The output is the yearly cost.

those are your corrected answers

Step-by-step explanation:

Answer:

Jessie scored higher than Reagan.

Step-by-step explanation:

We are given that Reagan scored 1140 on the SAT. The distribution of SAT scores in a reference population is normally distributed with mean 1000 and standard deviation 100.

Jessie scored 30 on the ACT. The distribution of ACT scores in a reference population is normally distributed with mean 17 and standard deviation 5.

For finding who performed better on the standardized exams, we have to calculate the z-scores for both people.

1. Finding z-score for Reagan;

Let X = distribution of SAT scores

SO, X ~ Normal([tex]\mu=1000, \sigma^{2}=100^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                                    Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 1000

            [tex]\sigma[/tex] = standard deviation = 100

Now, Reagan scored 1140 on the SAT, that is;

       z-score  =  [tex]\frac{1140-1000}{100}[/tex]  =  1.4

2. Finding z-score for Jessie;

Let X = distribution of ACT scores

SO, X ~ Normal([tex]\mu=17, \sigma^{2}=5^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                                    Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 17

            [tex]\sigma[/tex] = standard deviation = 5

Now, Jessie scored 30 on the ACT, that is;

       z-score  =  [tex]\frac{30-17}{5}[/tex]  =  2.6

This means that Jessie scored higher than Reagan because Jessie's standardized score was 2.6, which is 2.6 standard deviations above the mean and Reagan's standardized score was 1.4, which is 1.4 standard deviations above the mean.

Answer:

D

Step-by-step explanation:

i beleive the answer is D

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Answer:

The average rate of change from year 0 to year 2 is

[tex]change = -0.0585[/tex]

The average rate of change from year 3 to year 6 is

[tex]change = -0.0129[/tex]

Step-by-step explanation:

The average rate of change describes the average rate at which gas price in dollars per gallon is changing with respect to time (years)

The given polynomial function is

[tex]y = -0.0058x^4 +0.05x^3 -0.086x^2 - 0.04x + 2.52[/tex]

Calculate the average rate of change from year 0 to year 2.

For year x = 0

[tex]y = -0.0058(0)^4 +0.05(0)^3 -0.086(0)^2 - 0.04(0) + 2.52 \\\\y = 2.52[/tex]

For year x = 2

[tex]y = -0.0058(2)^4 +0.05(2)^3 -0.086(2)^2 - 0.04(2) + 2.52 \\\\y = -0.0928 + 0.4 - 0.344 - 0.08 + 2.52 \\\\y = 2.403[/tex]

The average rate of change from year 0 to year 2 is

[tex]change = \frac{y(2) - y(0)}{x(2) - x(0)} \\\\change = \frac{ 2.403- 2.52}{2 - 0} \\\\change = \frac{-0.117}{2} \\\\change = -0.0585[/tex]

The negative sign indicates that the gas price has decreased from year 0 to year 2.

The average rate of change from year 3 to year 6 is

For year x = 3

[tex]y = -0.0058(3)^4 +0.05(3)^3 -0.086(3)^2 - 0.04(3) + 2.52 \\\\y = -0.4698 + 1.35 - 0.774 - 0.12 + 2.52 \\\\y = 2.506[/tex]

For year x = 6

[tex]y = -0.0058(6)^4 +0.05(6)^3 -0.086(6)^2 - 0.04(6) + 2.52 \\\\y = -7.5168 + 10.8 - 3.096 - 0.24 + 2.52 \\\\ y = 2.4672[/tex]

The average rate of change from year 3 to year 6 is

[tex]change = \frac{y(6) - y(3)}{x(6) - x(3)} \\\\change = \frac{ 2.4672- 2.506}{6 - 3} \\\\change = \frac{-0.0388}{3} \\\\change = -0.0129[/tex]

The negative sign indicates that the gas price has decreased from year 0 to year 2.

Answer:

[tex]g(x) = \frac{1}{5} |x|[/tex]

Step-by-step explanation:

Given

[tex]f(x) = |x|[/tex]

Vertically compressed

Compression Factor = 5

Required

Find the equation of the new function;

Let the new function be represented by g(x)

Let c represented the compression factor;

such that c = 5

When a function f(x) is vertically compressed by factor c, the new function becomes

[tex]f(\frac{1}{c}x)[/tex]

From properties of functions;

[tex]f(\frac{1}{c}x) = \frac{1}{c} *f(x)[/tex]

This implies that

[tex]g(x) = f(\frac{1}{c}x) = \frac{1}{c} *f(x)[/tex]

[tex]g(x) = \frac{1}{c} *f(x)[/tex]

Recall that [tex]f(x) = |x|[/tex] and c = 5

[tex]g(x) = \frac{1}{5} * |x|[/tex]

[tex]g(x) = \frac{1}{5} |x|[/tex]

Hence, the new function is [tex]g(x) = \frac{1}{5} |x|[/tex]

Answer:

G(x)=1/5 |x|

Step-by-step explanation:

A p e x

Answer:

Y = 2

E = 9

A = 1

R = 0

Step-by-step explanation:

2222 - 999 + 11 - 0 =1234

Answer: 1 is not, 2 is, 3 is, 4 is, 5 is, 6 is not

Step-by-step explanation:

1 is not because 2 has two arrows coming off of it and each input can only have one output. 6 is not because if you draw a line down the graph it will hit the figure more than once( this is called the pencil drop test)

Function is an assignation that for each element of first set assigns one and only one element from second set.

1) NO    {element 2 from set one has assigned two elements (b, c) from set two}

2)  YES

3) YES     {several elements from set one can have assigned the same element from set two}

4), 5)   YES

6)  NO   {for x from about -4 to about 0.5 there are two y}

Answer:

11

Step-by-step explanation:

7x-4=73

7x = 4+73

7x = 77

7x/7 = 77/7

x = 11

Answer It is the first option because it has reflectional symmetry vertically and horizontally, therefore creating 4 lines of symmetry. If that's wrong, then it's "c."

Step-by-step explanation:

because it has reflectional symmetry vertically and horizontally, therefore creating 4 lines of symmetry. If that's wrong, then it's "c."

[tex]answer \\ = 5 \sqrt{17} \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

4

Step-by-step explanation:

Month 1- average rating as er graph is 4 point (1,4)

Rating was 4 at the beginning, then was stable for 2 months at 3, then increased over time up to 8 at month 10, point (10, 8)

Answer:

x⁴ + x³ + 4x² - 5x

Step-by-step explanation:

The polynomials given in the question are:

x⁴ - 3x + 1

4x² - 2x + 8

x³ - 9

We have to add all them

First write all the polynomial in the summation form:

(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)

Open the brackets:

x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9

Group together the similar terms

(x⁴) + (x³) + (4x²) + (-3x -2x) + (1 + 8 - 9)

Finding the sum in brackets:

x⁴ + x³ + 4x² + (-5x) + (0)

x⁴ + x³ + 4x² - 5x

Note that the sum is in descending powers of x

Step-by-step explanation:

because we know that both of these parts have to do with right triangles, we know that we can use the Pythagorean theorem.

since q is the right angle, you know that any line segment with q is a leg of the triangle

A.)

a^2 + b^2 = c^2 (add in values)

8^2 + 15^2 = c^2  (a=pq and b=qr) SIMPLIFY

64 + 225 = 289 (add)

find the square root of 289 = 17 so pr = 17

B.

This time we are using one leg (pq) and the hypotenuse (pr) to find the other leg

a^2 + b^2 = c^2 (sub the numbers in)

a^2 + 8^2 = 10^2 (simplify)

a^2 + 64 = 100 (subtract 64 on both sides)

a^2 = 36

the square root of 36 is 6 so qr = 6

Answer:

John's initial investment is Rs.150000

Step-by-step explanation:

Let the principal amount be a

We are given that John wants to invest in a simple interest savings account .The interest rate on this account is 0.7%.

Now to find simple interest in x years

Formula : [tex]Si = P \times T \times R[/tex]

Where P = Principal

T= time

R = rate of interest in decimals

So,[tex]SI=a \times 0.007 \times x[/tex]

Amount = Principal+Interest

Amount = [tex]a+a(0.007)x[/tex]

We are given that The account balance y can be modeled by the following linear equation y=150,000+150,000(0.007)x

So, On comparing a = 150000

Hence John's initial investment is Rs.150000

This question is incomplete because it was not written properly

Complete Question

A teacher gave his class two quizzes. 80% of the class passed the first quiz, but only 60% of the class passed both quizzes. What percent of those who passed the first one passed the second quiz? (2 points)

a) 20%

b) 40%

c) 60%

d) 75%

Answer:

d) 75%

Step-by-step explanation:

We would be solving this question using conditional probability.

Let us represent the percentage of those who passed the first quiz as A = 80%

and

Those who passed the first quiz as B = unknown

Those who passed the first and second quiz as A and B = 60%

The formula for conditional probability is given as

P(B|A) = P(A and B) / P(A)

Where,

P(B|A) = the percent of those who passed the first one passed the second

Hence,

P(B|A) = 60/80

= 0.75

In percent form, 0.75 × 100 = 75%

Therefore, from the calculations above, 75% of those who passed the first quiz to also passed the second quiz.

Answer:

x=54 degrees

Step-by-step explanation:

These two angles are complementary, meaning that they add to 90 degrees.

If one angle is 36 degrees, then we can write this equation: 36+x=90

We want to find what x is, so we should isolate x.

We can isolate x by subtracting 36 on both sides.

x=90-36

x=54

Answer:

54°

Step-by-step explanation:

∠PQR +∠RQS =∠PQS

36° + x° = 90°

x = 90 - 36 = 54°

Answer:

A & F

Step-by-step explanation:

if you look at the other question I answered for you, you can see the work. but basically you can figure out slope by doing m=y2-y1/x2-x1.

so we now know the slope is 1/4. which eliminates choices B, D, E.

we see that C will not work because the x and y values are switched.

according to point slope formula A & F work.

Answer:

D.  Yes by SAS Similarity Postulate

Step-by-step explanation:

This is the answer because if you flip triangle LNM around to shape the DEF.  Then you will see that:

1. angle D is congruent to angle L

2. angle E is congruent to angle N

3. angle F is congruent to angle M

4. angle E and N are both 90 degrees

Because (DE and LN) and (MN and FE) are similar and (E and N) are 90 degrees, then we do not need (FD and ML) to tell if triangle DEF and triangle LNM is similar or not. They are similar.

We next need to figure out if the triangles are similar by SSS (Side-side-side) Similarity Postulate or SAS (side-angle-side) Similarity Postulate.  The SAS Similarity Postulate states that if you have 2 similar sides and 1 congruent angle, then the two shapes are similar. Right now we have 2 similar sides in (DE and LN) and (MN and FE) and 1 congruent angle that are both 90 degrees. This follows all the rules of the SAS Similarity Postulate, so that means that these two triangles are similar by SAS Similarity Postulate.

Answer:

D. SAS Similarity Postulate

Step-by-step explanation:

I got it right on the test

Answer:

24.3 units (3 s.f.)

Step-by-step explanation:

Since a square has 4 equal sides,

perimeter of ABCD= 4(length of AB)

Distance between 2 points

=[tex] \sqrt{(y1 - y2)^{2} + (x1 - x2)^{2} } [/tex]

Length of AB

[tex] = \sqrt{( { - 2 - 4)}^{2} + {(2 - 3)}^{2} } \\ = \sqrt{( - 6)^{2} + ( - 1)^{2} } \\ = \sqrt{37} [/tex]

perimeter of ABCD

[tex] = 4 \sqrt{37} \\ = 24.3 \: units \: (3 \: s.f.)[/tex]

Answer:

1783 sq. Units

Step-by-step explanation:

Answer:

[tex]-1868[/tex]

Step-by-step explanation:

[tex]-165 - 1703[/tex]

Subtract the numbers.

[tex]=-1868[/tex]

Answer:

-1868 is the simplified polynomial

Step-by-step explanation:

-165 -1703

= -165 + -1703

= -(165+1703)

= -(1868)

Answer:

Step-by-step explanation:

k den

Answer:

1 / 4 (2x − 14) = 4.

Multiply through by 4(2x - 14)

You'll get

1 = 16(2x - 14)

1 = 32x - 224

Group like terms

224 + 1 = 32x

225 = 32x

Divide both sides by 32

x = 225/ 32

Hope this helps

Answer:

add a picture

Step-by-step explanation:

Answer:

a is the answer

have a great day. brainliest please

Step-by-step explanation:

Answer:

the answer is A. :)

Step-by-step explanation:

the answer A. is 10 so just think what 2 times what will equal 10 so....2 x 5 = 10 and we got 10 so that is how we get our answer

Brainliest please thank you! and good luck!

Answer:

x = 20

y = 73

Step-by-step explanation:

8x - 87 + 7x - 33 = 180

15x = 180 + 87 + 33

15x = 300

x = 20

8x - 87 = y

160 - 87 = y

y = 73

Answer:

13divided by 7

Step-by-step explanation:

[tex]4x + 3x - 4 = 17 \\ 7x - 4 = 17 \\ 7x = 17 - 4 \\ 7x = 13 \\ \frac{7x}{7} = \frac{13}{7 } \\ x = \frac{13}{7} or1 \times \frac{6}{7} [/tex]

The required number is 3 .

It is required to find the number.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

Let the number be x

According to given question we have,

4x+3x-4=17

Compare the like terms we get,

7x=17+4

7x=21

x=3

The number is 3 .

Therefore, the required number is 3 .

Learn more details about algebra here:

https://brainly.com/question/24875240

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