Rahmi bought 1 pair of jeans and 2 T-shirts. How much did rahmi spend? Write equations to solve. Use a letter to represent the unknown quantity

There are several ways to prove a mathematical statement. These ways include: by contradiction, by induction, contraposition, etc

To prove the statement, we make use of proof by contradiction

From the question:

x is a composite number such that: x > 1

This means that 1 < a < x is a factor of x

This can be represented as:

[tex]x = a * b[/tex]

Where:

Assume that b is less than or equal to a.

Also, let

[tex]b > \sqrt x[/tex]​

This means that:

[tex]\sqrt x < b \ge a[/tex]

The above becomes

[tex]\sqrt x < a[/tex]

Rewrite as:

[tex]a > \sqrt x[/tex]

So, we have:

[tex]x = a * b > \sqrt x * \sqrt x = x[/tex]

The above means that:

[tex]x > x[/tex]

The above inequality is a contradiction because, a number x cannot be greater than itself

This means that, the supposition is wrong.

Hence, the given statement has been proved by contradiction

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Answer:

45

Step-by-step explanation:

30/2=15 +30=45

Answer:

The Jacobson Animal Shelter has 45 total animals.

Step-by-step explanation:

dogs = 30

cats = 30/2

cats = 15

dogs + cats = total

30 + 15 = total

45 = total

Answer:

$9.93

Step-by-step explanation:

sorry if it doesn't help.

Answer:

The answer is 45

Step-by-step explanation:

135 and 225

Here, 225 > 135

225 = 135 × 1 + 90

Since remainder ≠ 0, we apply division Lemma to 135 and 90

135 = 90 × 1 + 45

Since remainder ≠ 0, we apply division Lemma to 90 and 45

90 = 45 × 2 + 0

Since remainder = 0, divisor 45 is the HCF

Thus, HCF (135, 225) = 45

-TheUnknownScientist 72

Answer:

HCF = 45

Step-by-step explanation:

225 = (135 × p) + q

⇒ 225 = (135×1) + 90

⇒ 135 = (90 × 1) + 45

⇒ 90 = (45 × 2) + 0

HCF (135, 225) = 45

Answer:

Step-by-step explanation:

Our expression given: 3(x-6) + 2y

A. Substitute x = -7 and y = 10 into the equation.

[tex]3( - 7 - 6) + 2(10)[/tex]

Use the Distributive Property:

[tex] - 21 - 18 + 20[/tex]

Solve:

[tex] - 19[/tex]

B. Substitute x = 5 and y = -2 into the equation.

[tex]3(5 - 6) + 2( - 2)[/tex]

Use the Distributive Property:

[tex]15 - 18 + -4[/tex]

Solve:

[tex]-7[/tex]

C. Substitute x = 0 and y = 6 into the equation.

[tex]3(0 - 6) + 2(6)[/tex]

Use the Distributive Property:

[tex] - 18 + 12[/tex]

Solve:

[tex]-6[/tex]

D. Substitute x = 3 and y = 3 into the equation.

[tex]3(3 - 6) + 2(3)[/tex]

Use the Distributive Property:

[tex]9 - 18 + 6[/tex]

Solve:

[tex]-3[/tex]

Answer:

Classes representing assets.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hey there!

-3(7 + 5g)

DISTRIBUTE -3 WITHIN the PARENTHESES

= -3(7) - 3(5g)

= -21 - 15g

= -15g - 21

Good luck on your assignment and enjoy day!

~Amphitrite1040:)

Solution:

Let's simplify each inequality one by one.

This means that...

Hoped this helped!

Answer:

The car travels 40 miles per hour. In 8hrs, the car will have droven 320 miles. In one hour the car will have have driven 40 miles. Step-by-step explanation:

Excuse me, but I believe this is a unit rate, so the first thing I did was was divide 120 by 3 to get the answer 40 for A. Then, since I knew that the car goes 40 miles per hour, I multiplied that by 8 to get 320 for B.

Answer:

The diffrence is 37 degrees

Step-by-step explanation:

30-(-7)=37  

Answer:

Step-by-step explanation:

A ratio can be expressed three (3) ways. The ratio of A to B can be expressed as any of ...

  A to B

  A : B

  A/B

It will be in reduced form when the numbers are mutually prime (have no common factors).

__

The ratio of burgers without onions to burgers with onions is ...

  without : with = 8 : 2 = 4 : 1

__

The ratio of history visitors (5) to science visitors (44) is ...

  history : science = 5 : 44

_____

Additional comment

Some problems can be fairly easily worked by considering the difference between A and B in the ratio A/B. However, those differences are irrelevant to this problem. Here, you're simply asked to write the ratios.

We note that the ratios asked for reverse the appearance of the numbers given in the problem. That is, the second number in the ratio requested is the number described first. This requires you pay attention to what you are given and what is requested. (That's always a good idea.)

$378 is 72% of the original price.

72% = $378

1% = $378/72

1% = $5.25

100% = $5.25(100)

100% = $525

The original price of the sofa is $525

Hope this helps!

Answer:

3 x 10^4

Step-by-step explanation:

the decimal is behind the 3 (3.) and you move the decimal 4 times to the right

Answer:

390 cubic centimeters

Step-by-step explanation:

the volume of a box is the length width and height all multiplied together

so this is what the equation would look like

5(6)(13)

you can split this up into

5(6) * 13

so 5(6) is 30

30(13)

this is 390

so the box is 390 cubic centimeters

Using a system of equations, it is found that the trains will be side by side in 15 seconds.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

[tex]y_1 = 229t[/tex]

[tex]y_2 = 149t + 1200[/tex]

They will be side-by-side when:

[tex]y_1 = y_2[/tex]

Hence:

[tex]229t = 149t + 1200[/tex]

[tex]80t = 1200[/tex]

[tex]t = \frac{1200}{80}[/tex]

[tex]t = 15[/tex]

The trains will be side by side in 15 seconds.

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Answer:

B

Step-by-step explanation:

do you watch anime

Option A

(81.25%,88.75%)

A confidence interval is how much instability there's with any specific statistic. Confidence intervals are frequently utilized with a margin of error. It tells you how confident you'll be able be that the results from a poll or survey reflect what you'd expect to find in the event that it were possible to survey the whole population. Confidence intervals are inherently associated to confidence levels.

Here the sample size, n=600

85% of the teachers polled felt that computers in the classroom were beneficial to students.

so the proportion=85%=0.85

Confidence level=99%

so. the level of significance, α=1-0.99=0.01

So, z critical value at 99% confidence level,

[tex]Z_{\frac{\alpha }{2} } =2.576[/tex]

So the formula to find confidence interval is,

[tex]proportion-Z_\frac{\alpha }{2} *\sqrt{\frac{prop.(1-prop)}{n} } < p < proportion+Z_\frac{\alpha }{2} *\sqrt{\frac{prop.(1-prop)}{n} }[/tex]

[tex]0.85-2.576*\sqrt{\frac{0.85*(1-0.85)}{600} } < p < 0.85+2.576*\sqrt{\frac{0.85*(1-0.85)}{600} }[/tex]

=(0.8125,0.8875)

=(81.25%,88.75%)

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Answer:

16 hours

Step-by-step explanation:

Let the mechanic works for x hours to make a money of $350.

Fixed charges = $30

Charges per hour = $20

So, charges for x hours = $20x

Total money earned = $350

[tex] \implies \: 20x + 30 = 350 \\ \\ \implies \: 20x = 350 - 30 \\ \\ \implies \: 20x = 320 \\ \\ \implies \: x = \frac{320}{20} \\ \\ \implies \: x = 16 \: hours[/tex]

Thus, the mechanic needs to work for 16 hours to make $350.

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

[tex]\mathsf{7.209\times10^{-4}}\\\\\mathsf{\approx 7.209\times\dfrac{1}{10\times10\times10\times10}}\\\\\mathsf{\approx 0.000721}\\\\\mathsf{\approx 7.21\times10^{-4}}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{7.21\times10^{-4}}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

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

Answer:

b) 0.09e

Step-by-step explanation:

9% is 9/100= 0.09 (e) =0.09e

a = amount deposited at 3.5%

b = amount deposited at 4.5%

we know that "b" is twice as much as "a", thus b = 2a.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.5\% of a}}{\left( \cfrac{3.5}{100} \right)a}\implies 0.035a \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.5\% of 2a}}{\left( \cfrac{4.5}{100} \right)2a}\implies 0.045(2a)[/tex]

we also know that whatever "a" amount is, their sum is 2250, thus

[tex]0.035a+0.045(2a) = 2250\implies 0.035a+0.09a=2250\implies 0.125a=2250 \\\\\\ a=\cfrac{2250}{0.125}\implies \boxed{a=18000}~\hspace{10em}\boxed{\stackrel{2a}{b=36000}}[/tex]

Step-by-step explanation:

y = 2x + 7

y = 2(–2) + 7 = 3

y = 2(–1) + 7 = 5

y = 2(0) + 7 =7

y = 2(1) + 7 = 9

y = 2(2) + 7 =11

Answer:

1. [tex]\frac{1}{4}[/tex]

2.[tex]\frac{3}{8}[/tex]

3.[tex]\frac{5}{8}[/tex]

4.[tex]\frac{3}{4}[/tex]

5.[tex]\frac{3}{8}[/tex]

6. [tex]\frac{0}{8}[/tex] or 0

7. [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Count the amount of each number and put it over 8.

Simplify if possible.

Answer:

[tex]{ \tt{16 {b}^{2} c {}^{12} - 0.25 }}[/tex]

» Change the decimal to a fraction:

[tex] = { \tt{ {16b}^{2} {c}^{12} - \frac{1}{4} }} \\ [/tex]

» Change the other degrees to indices;

[tex] = { \tt{ \blue{( {4}^{2}) }} {b}^{2} {c}^{12} - \frac{1}{ \red{( {2}^{2} )}} } \\ \\ = { \tt{ {(4bc {}^{6} )}^{2} - \frac{1}{4} }}[/tex]

» Factorize:

[tex] = { \tt{4}^{2} \{ ( {bc}^{6} ) {}^{2} - \frac{1}{4} \}} \\ \\ { \boxed{ \tt{ = 16 \{ { \blue{{(bc}^{6}) {}^{2} - \frac{1}{4} } \}}}}}[/tex]

Answer:

This statement shows the Commutative Property of Multiplication. It basically says that now matter order in which you multiply, you still have the same answer because, for example, 4*5=5*4. You can multiply 4 by 5 but you could also multiply 5 by 4 because multiplication is commutative. :)

Step-by-step explanation:

Just add a similar triangle from the opposite side

Then what happens

Now

Area

[tex]\\ \tt\hookrightarrow LB=5(4)=20[/tex]

Answer:

Length = 5

Width = 4

Area = 20

Triangle area = 10

Step-by-step explanation:

The length of the rectangle = the longest leg = 5 units

The width of the rectangle = the shortest leg = 4 units

The area of the rectangle = width x length = 4 x 5 = 20 units²

The area of the triangle = 1/2 the area of the rectangle = 20 ÷ 2 = 10 units²

Answer:

Step-by-step explanation:

$50050050re=$450(1+2re)=450+900re=900re=50900=0.05555¯=5.555¯%

The amount of interest will be $50 for the investment.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.

Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.

Given that Krisi took out a $500 discounted loan calculated using a simple interest rate of 5% for a period of 2 years.

The interest will be calculated as:-

SI = ( 500 x 5 x 2 ) / 100

SI = $50

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Answer:

69f

Step-by-step explanation: