Question 4 Multiple Choice Worth 1 points)
(04.02 LC)
What is the solution to the following system of equations?
X - 3y = 5
2x + y = 10
(5,0)
(0,5)
(7,0)
(0,7)

Answer: the answer is C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It's like connecting the dots

For example, BD. When you draw a line from B to D, you have to touch O at some point.

That happens for all of them except one, which is a.) AB.

When you connect points A and B, you never touch point O

Edit; What the other person said is right actually. I'm wrong. He gets my 5 stars.

If the combined weight is 1.5 kilograms and the weight of the gram weights is 0.5 kilograms, then the mass of the object is 1 kilogram.

Mass is describes the amount of matter it contains. It is usually measured in kilograms or pounds. Mass is distinct from weight, which measures the force of gravity on an object.

To measure the mass of an object that I think has a mass greater than 1 kilogram, I will use a pan balance and kilogram and gram weights.

First, I will set the pan balance to 0 by adjusting the counterweight.

Then, I will place the object on one of the pans and add weights to the other pan until the balance is equal.

I will first use 1 kilogram weights and then add smaller gram weights until the pan balance is equal.

Once the pan balance is equal, the combined weight of the object and the weights will be the mass of the object.

I can then calculate the mass in kilograms by subtracting the weight of the gram weights from the total mass.

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Answer:

The profit that Jamal made was $61.50

Step-by-step explanation:

125.00-63.50= 61.50

Answer:

a. C = $ 10.50x b. 2 persons

Step-by-step explanation:

a. Write an equation to find how many people visited in a hour

Let x be the number of persons admitted in one hour. Since the movie theater charges 10.50 per person for admission, then the total admission fees would be C = charge per person × number of persons = $ 10.50 × x = $ 10.50x.

C = $ 10.50x

b. Solve an equation to find how many people visited in a hour

Given that C = $19.11, and C = $ 10.50x, so,

x = C/($10.50)

substituting C into the equation, we have

x = $19.11/$10.50

x = 1.82

Since we cannot have a decimal number of persons, x is rounded up to the nearest whole number. So,

x = 1.82

x ≅ 2

So, two people visited the theater in one hour.

The parametric equations for the tangent line to the curve with the given parametric equations at the specified point is  \(e^{(-2t)\)cos(3t), y =  \(e^{(-2t)\)sin(3t), z = \(e^{(-2t)\)

To find the parametric equations of the tangent line to a curve with given parametric equations at a point, we need to follow the following steps:

Let's apply these steps to the given problem:

Find the derivatives dx/dt, dy/dt, and dz/dt of the given parametric equations:

\(dx/dt = -2e^{(-2t)}cos(3t) - 3e^{(-2t)}sin(3t)\)

\(dy/dt = -2e^{(-2t)}sin(3t) + 3e^{(-2t)}cos(3t)\)

dz/dt = -2e^(-2t)

Plug in the value of t that corresponds to the given point (1,0,1) to find the corresponding values of dx/dt, dy/dt, and dz/dt:

dx/dt(1) = -2e⁻² ¹ cos(3(1)) - 3e⁻²  ¹ sin(3(1)) = -5.348

dy/dt(1) = -2e⁻² ¹ sin(3(1)) + 3e⁻² ¹)cos(3(1)) = 2.317

dz/dt(1) = -2e⁻² ¹ = -1.471

Use the point (1,0,1) and the values of dx/dt, dy/dt, and dz/dt at that point to write the equation of the tangent line in parametric form. Let's call the parametric equation of the tangent line (x(t), y(t), z(t)):

x(t) = 1 - 5.348(t-1)

y(t) = 0 + 2.317(t-1)

z(t) = 1 - 1.471(t-1)

Therefore, the parametric equations of the tangent line to the curve x =  \(e^{(-2t)\)cos(3t), y =  \(e^{(-2t)\)sin(3t), z = \(e^{(-2t)\) at the point (1,0,1) are x(t) = 1 - 5.348(t-1), y(t) = 2.317(t-1), z(t) = 1 - 1.471(t-1).

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After 24 days, there will be approximately 25 atoms of I13153 remaining. The nuclear process that occurs during the decay is the transformation of I13153 into Xe13154.

The half-life of I13153 is nearly 8 days, which means that after each 8-day period, half of the atoms will decay into Xe13154. Starting with a sample of 200 atoms of I13153, we can calculate the number of remaining atoms after 24 days. Since the half-life is 8 days, the number of remaining atoms after each 8-day period is halved. After the first 8 days, there will be 100 atoms of I13153 remaining.

After the second 8 days, there will be 50 atoms remaining. And after the third 8 days, there will be 25 atoms of I13153 remaining. The nuclear process that occurs during the decay of I13153 is radioactive decay. Specifically, it undergoes beta decay, where a neutron in the nucleus of I13153 is converted into a proton, resulting in the formation of Xe13154. This process releases radiation and transforms the original isotope into a different element.

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Answer:

no idea- I would say the answer is 4 but i don't know if the triangles are similar or not

Step-by-step explanation:

Answer:

Step-by-step explanation:

What Math skill is that ?

i might be able to help you

The value of ACD of a trapezium is 26.56°.

Let ABCD be a trapezoid with BCǀǀAD and AB=BC=CD= ½ AD.

ACD can be determined by using the Pythagorean theorem or using the theorem of Pythagoras.

The theorem of Pythagoras states that if you draw a right-angled triangle with the hypotenuse as c and the legs a and b.

The sum of squares of the legs (a and b) equals the square of the hypotenuse (c).

Therefore, by using the Pythagorean theorem ; AC² = AB² + BC²

=> AC² = (1/2 AD)² + (1/2 AD)²

=> AC² = 1/4 AD² + 1/4 AD²

=> AC² = 1/2 AD².

Hence,AC² = 1/2 AD²

ACD is a right-angled triangle where AC is the hypotenuse.

Thus, using the theorem of Pythagoras, we can write: AD² = AC² + CD²

=> AD² = [√(1/2 AD²)]² + (AD/2)²

=> AD² = 1/2 AD² + 1/4 AD²

=> AD² = 3/4 AD²=> AD = √4/3 AD

Thus, ACD=ACD = tan¯¹(√1/2 AD²/AD/2) = tan¯¹(√2/4) = 26.56°

Therefore, ACD is 26.56°.

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Answer:

B = 50

Step-by-step explanation:

\(\frac{5}{10} =\frac{b}{100}\)   do butterfly multiplication

\(5*100=500\)

\(10*b=10b\)

\(\frac{10b}{10}=\frac{500}{10}\)

B = 50

Answer: B. C(n)=0.75n-0.25

Hope these helped u :)

Step-by-step explanation:

Answer: I believe it's B because 1 candy bar=0.75 but there's a $0.25 percent off so I think 0.75n-0.25 would be the right answer

Step-by-step explanation:

Answer:

\(y \geq -4\)

Step-by-step explanation:

This is because the lowest the y-coordinate goes to is -4.

The probability that a patient with a stiff neck has meningitis is very low at 0.002%.

To find the probability that a patient with a stiff neck has meningitis, we can use Bayes' theorem.

Let A be the event that the patient has meningitis and B be the event that the patient has a stiff neck.

We know that P(B|A) = 0.5, meaning that if a patient has meningitis, there is a 50% chance they will have a stiff neck. We also know that P(A) = 1/50,000, meaning that the probability that any patient has meningitis is 1 in 50,000. Additionally, we know that P(B) = 1/20, meaning that the probability that any patient has a stiff neck is 1 in 20.

Using Bayes' theorem, we can find the probability that a patient with a stiff neck has meningitis:

P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 0.5 * (1/50,000) / (1/20)
P(A|B) = 0.00002 or 0.002%

Therefore, the probability that a patient with a stiff neck has meningitis is very low at 0.002%.

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Answer:

Amy has 12 5¢ coins

Step-by-step explanation:

Let x represent 20¢ coins and y represent 5¢ coins.

Amy has four more 20¢ coins than 5¢ coins. Hence:

\(x=y+4\)

And the total value of all her coins is $3.80. Thus:

\(0.2x+0.05y=3.8\)

This yields a system of equations:

\(\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}\)

We can solve by substitution. Substitute the first equation into the first:

\(\displaystyle 0.2(y+4)+0.05y=3.8\)

Distribute:

\(\displaystyle 0.2y+0.8+0.05y=3.8\)

Combine like terms:

\(\displaystyle 0.25y = 3\)

And divide both sides by 0.25. Hence:

\(y=12\)

Thus, Amy has 12 5¢ coins.

Using the first equation:

\(x=y+4\)

Substitute:

\(x=(12)+4=16\)

Thus, Amy has 16 20¢ coins.

In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.

The amount that Xavier Knox's employer deducts from his paychecks for state income tax is b. $83.27

First find his taxable income:

= Annual salary - Personal exemptions

= 61, 100 - 4, 000

= $57, 100

The state income tax per year is:

= 57, 100 x 3.5% state income tax rate

= $1, 998.50

The semimonthly state income tax deducted is:
= 1, 998.50 / (12 months x twice a month)

= $83.27

In conclusion, on a semimonthly basis, $83.27 is deducted for state income tax.

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Answer:

x < -3

Step-by-step explanation:

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Converted (a) 2.2 kg = 77.6 oz, 4.83 lbm. (b) 12 lbf/in2 = 82.7 kPa, 620.6 mmHg. (c) 160 hp = 119,360 cal/s, 88,000 Btu/s. (d) 82 gallons = 328 quarts, 313,981.8 mL. (e) 34 in = 0.8636 m, 86.36 cm.

What is conversion factor ?

A conversion factor is a ratio of two equivalent measurements used to convert a quantity from one unit to another.

(a) To convert 2.2 kg to ounces, we can use the conversion factor 1 kg = 35.274 oz. So, 2.2 kg = 2.2 * 35.274 oz = 77.6 oz. To convert 2.2 kg to lbm, we can use the conversion factor 1 kg = 2.205 lbm. So, 2.2 kg = 2.2 * 2.205 lbm = 4.83 lbm.

(b) To convert 12 lbf/in2 to kPa, we can use the conversion factor 1 lbf/in2 = 6.894 kPa. So, 12 lbf/in2 = 12 * 6.894 kPa = 82.7 kPa. To convert 12 lbf/in2 to mmHg, we can use the conversion factor 1 lbf/in2 = 51.715 mmHg. So, 12 lbf/in2 = 12 * 51.715 mmHg = 620.6 mmHg.

(c) To convert 160 hp to cal/s, we can use the conversion factor 1 hp = 746 cal/s. So, 160 hp = 160 * 746 cal/s = 119,360 cal/s. To convert 160 hp to Btu/s, we can use the conversion factor 1 hp = 550 Btu/s. So, 160 hp = 160 * 550 Btu/s = 88,000 Btu/s.

(d) To convert 82 gallons to quarts, we can use the conversion factor 1 gallon = 4 quarts. So, 82 gallons = 82 * 4 quarts = 328 quarts. To convert 82 gallons to mL, we can use the conversion factor 1 gallon = 3785.4 mL. So, 82 gallons = 82 * 3785.4 mL = 313,981.8 mL

(e) To convert 34 in to m, we can use the conversion factor 1 in = 0.0254 m. So, 34 in = 34 * 0.0254 m = 0.8636 m. To convert 34 in to cm, we can use the conversion factor 1 in = 2.54 cm. So, 34 in = 34 * 2.54 cm = 86.36 cm.

Converted (a) 2.2 kg = 77.6 oz, 4.83 lbm. (b) 12 lbf/in2 = 82.7 kPa, 620.6 mmHg. (c) 160 hp = 119,360 cal/s, 88,000 Btu/s. (d) 82 gallons = 328 quarts, 313,981.8 mL. (e) 34 in = 0.8636 m, 86.36 cm.

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Answer:

\( \huge{ \boxed{ \text{ i. \: \ - 7x}}}\)

\( \huge{ \boxed{ \text{ii. \: 23a}}}\)

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☄ Question : Subtract the following using horizontal method :

✎ Step - by - step Explanation :

In horizontal method , terms are arranged in same row and put sign for subtraction and remove the brackets and then simplify.

\( \longrightarrow{ \sf{ - 5x - (2x)}}\)

\( \longrightarrow{ \sf{ - 5x - 2x}}\)

Like terms can be added or subtracted. Only coefficients of like terms can be added or subtracted.

\( \longrightarrow{ \boxed{\sf{ - 7x}}}\)

Likewise , Let's do next too:

\( \dashrightarrow{ \sf{ 18a - ( - 5a)}}\)

Remember : \( \sf{( - ) \times ( - ) = ( + )}\)

\( \dashrightarrow{ \sf{ 18a + 5a}}\)

\( \dashrightarrow{ \boxed{ \sf{ 23a}}}\)

And we're done!

Hope I helped!

Have a wonderful time ツ

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Answer:

i)-7x ii)23a

Step-by-step explanation:

i)U well get -5x-2x, after solving, u well get -7x since all is negetive. ii)U well get 18a-(-5a) which u well get 18a+5a whict is equal to 23a

Answer:

B.

Step-by-step explanation:

Dilation changes the size of the triangle but not the shape so the image is similar.

A, C and D creates congruent triangle.

The conclusion is that the expression \(\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}\) cannot be solved  without the l'hopital's rule,

The limit expression is given as:

\(\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}\)

The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞

i.e.

\(\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}\)

So, the best way is to apply the l'hopital's rule.

This is done as follows:

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}\)

When the numerator and the denominator are differentiated, we have:

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}\)

Further, differentiate

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}\)

Now, we can substitute \(\infty\) for x

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}\)

Evaluate the numerator

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}\)

Evaluate the quotient

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty\)

Hence, the conclusion is that the expression \(\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}\) cannot be solved  without the l'hopital's rule

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Answer:

The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Step-by-step explanation:

By applying the distributive law to this equation, we can produce the equation :

     4x − 12 − 5x − 5 = 3;

The distributive property is a mathematical function in which each element in the parentheses is multiplied by the one outside of it;

   4(x − 3) − 5(x + 1) = 3

In the equation;

  4 distribute over the first parentheses and -5 over the second one;

   So we expand;

      4x - 13 - 5x -5  = 3

In distributive property, expansion simply takes place.

The correct option is "Reject the claim that community college students pay more than $1,250 per year on textbooks when the actual amount that community college students pay for textbooks is actually more than $1,250 per year." is the hypothesis test statement that is a Type I Error.

Type I error is defined as the error of rejecting the null hypothesis when it is true. This error is also called an alpha error because it has a certain level of probability of occurring. The hypothesis statement that constitutes a Type I Error is the one where we reject the claim that community college students pay more than $1,250 per year on textbooks when the actual amount that community college students pay for textbooks is actually more than $1,250 per year. Hence, option 1, "Reject the claim that community college students pay more than $1,250 per year on textbooks when the actual amount that community college students pay for textbooks is actually more than $1,250 per year." is the hypothesis test statement that is a Type I Error. In this case, we will end up rejecting the null hypothesis when it was true. This error can be reduced by increasing the sample size, by increasing the significance level, or by increasing the power of the test.

The significance level is the probability of making a Type I Error, denoted by alpha (α). The significance level is usually set at 0.05 or 0.01. The power of the test is the probability of correctly rejecting the null hypothesis when it is false. Hence, the null hypothesis cannot be rejected. The Type I Error rate is always set before the experiment is conducted. Answer: Type I error is defined as the error of rejecting the null hypothesis when it is true. The hypothesis statement that constitutes a Type I Error is the one where we reject the claim that community college students pay more than $1,250 per year on textbooks when the actual amount that community college students pay for textbooks is actually more than $1,250 per year.

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Answer:

214 ºF is the lowest temperature

Step-by-step explanation:

Temperature range of six degrees above or below 220°F:

This means that it should be brewed properfly between

220 - 6 = 214 ºF

and

220 + 6 = 226 ºF

214 ºF is the lowest temperature

226 ºF is the highest temperature.

Answer:

1/11

Step-by-step explanation:

Given:

Bonnie has 4 sharpened and 8 unsharpened pencils in her pencil case. she randomly selects 2 of the pencils from the box without replacement.

Question to Answer:

what is the probability that both pencils will be sharpened?

Solve:

Probability is possibility of an event being equal to the ratio of the number of outcomes and the total number of outcomes.

Thus we known that,

Bonnie has 4 sharpened and 8 unsharpened pencils.

Hence, the total numbers of pencils is 12.

Let, the probability first one is sharpened be P(E₁) and  probability second one is sharpened be P(E₂)

Simplify - P(E₁) = 4/12 = 1/3       and      P(E₂) = 3/11

Therefore we have;

P(E) = P(E₁)×P(E₂)

P(E) = 1/3 × 3/11

P(E) = 3/33

P(E) = 1/11

As a result, the probability is 1/11 that both pencils will be sharpened.

Kavinsky

Answer:

99.

Step-by-step explanation:

            99.0

          ___________

          |9801.000000

       9 |81

    189 | 1701

           | 1701

             ,,,,,

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

Answer:

Due to the high number of deaths and the subsequent population reduction, the merchants - and tradespeople in general - saw a decrease in the sales of their merchandise. Once the number of infected people by the plague reduced was reduced at the end of the Fifteenth Century, the population grew exponentially, thus creating a higher demand for services and goods.