How can unit analysis help you solve a conversion problem?

The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

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Answer:  6.992 gallons

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Given:  \(\textsf{895 oz}\)

Find: \(\textsf{Convert to gallon}\)

Solution:  We need to convert the fluid ounces of the drink to gallons.  We know that there are 128 fluid ounces in one gallon.  Therefore, we just need to multiply 895 oz by 1/128 to get our final answer.

Multiply by 1/128

Therefore, the final solution is that 895 fluid ounces is 6.992 gallons.

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

9514 1404 393

Answer:

  b. 327,449

Step-by-step explanation:

Adjacent digits have values related by a factor of 10 if they are the same digit.

  327,449

is the number that has two adjacent digits the same.

well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

Let's evaluate the equation and check if it satisfies the equality:`

6x + 4y = 36

6(3) + 4(4) = 36

18 + 16 = 36

34 ≠ 36

When x = 3 and y = 4 equality is not satisfied

The equation 6x + 4y = 36 is not valid for solutions x = 3 and y = 4.

Given data:

To determine if the solution (x = 3, y = 4) satisfies the equation 6x + 4y = 36, substitute the given values of x and y into the equation and then simplify to see if both sides are equal.

Given equation: 6x + 4y = 36

Substitute x = 3 and y = 4:

6(3) + 4(4) = 18 + 16 = 34

Now, compare the left-hand side and the right-hand side:

Left-hand side: 6x + 4y = 34

Right-hand side: 36

Since the left-hand side (34) is not equal to the right-hand side (36), the solution (x = 3, y = 4) does not satisfy the equation 6x + 4y = 36.

Hence, the equation 6x + 4y = 36 is not valid for x = 3 and y = 4.

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Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

Answer:

\(cosC = \frac{\sqrt{161} }{15}\)

Step-by-step explanation:

\(cosC = \frac{\sqrt{161} }{15}\)

CosC = adj/hyp

The grams of cocoa does it contains is 36.57 grams

From the question, we have the following parameters that can be used in our computation:

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

Substitute the known values in the above equation, so, we have the following representation

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer:

Any equation shown in the explanation

Step-by-step explanation:

Hello!

Combining like terms means combining terms with the same variables.

So combing all x's, all y's, all numbers, etc.

2/3x - 9 - 2x + 2 = 1

combine the x's

-1 1/3 x - 9 + 2 = 1

combine normal numbers

-1 1/3 x - 7 = 1

Add 7 to both sides

-1 1/3x = 8

Make mixed number into improper fraction

-4/3x = 8

Multiply both sides by 3

-4x = 24

Divide both sides by -4

x = -6

The answer would be any of the equation I showed above

Hope this helps!

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Answer: 96

Step-by-step explanation:

25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes

what is percent  ?

A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".

In the given question,

Let's assume that there are 100 people in Math town.

60% of them are males, so there are 60 males and 40 females.

Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.

28% of the entire population have brown eyes, so there are 28 people with brown eyes.

To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:

28 - 18 = 10

So, there are 10 females with brown eyes.

Out of the 40 females in Math town, what percentage have brown eyes?

10 brown-eyed females out of 40 females is:

10/40 = 0.25 or 25%

Therefore, 25% of the females in Math town have brown eyes.

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Probability, data, trends, likelihoods, and statistics are extensively utilized in veterinary medicine for disease surveillance, diagnostic testing, clinical research, drug efficacy evaluation, risk assessment, and predictive modeling. By employing given tools, veterinarians can make evidence-based decisions, enhance patient care, and improve overall animal health outcomes.

Probability, data, trends, likelihoods, and statistics are used in various aspects of veterinary medicine to inform decision-making, assess risk, and improve patient outcomes.

Here are some specific examples:

Epidemiology and Disease Surveillance: Veterinarians use probability and statistics to track and analyze disease trends in animal populations. By collecting and analyzing data on disease occurrence, veterinarians can identify patterns, determine risk factors, and develop strategies for prevention and control.

Diagnostic Testing: Veterinary medicine often relies on diagnostic tests to detect and confirm the presence of diseases in animals. Probability plays a crucial role in interpreting test results. Veterinarians use statistics to determine the sensitivity (the probability of a positive test result given that the disease is present) and specificity (the probability of a negative test result given that the disease is absent) of different tests. These measures help assess the accuracy and reliability of diagnostic tests and guide treatment decisions.

Clinical Research and Evidence-Based Medicine: Probability, data, and statistics are fundamental in conducting clinical research in veterinary medicine. Researchers use statistical analysis to evaluate the effectiveness of treatments, compare different interventions, and assess clinical outcomes. This allows veterinarians to make evidence-based decisions when selecting treatments and managing patients. Additionally, statistics help determine sample sizes, calculate confidence intervals, and perform statistical tests to determine the significance of research findings.

Pharmacology and Drug Efficacy: Probability and statistics are used to assess the effectiveness and safety of medications in veterinary medicine. Clinical trials employ statistical methods to determine the optimal dosage, evaluate drug interactions, and assess the likelihood of adverse effects. These statistical analyses help veterinarians understand the benefits and risks associated with specific drugs, enabling them to make informed decisions when prescribing medications.

Risk Assessment and Predictive Modeling: Veterinarians often use probability and statistics to assess risks and predict outcomes in various scenarios. For example, when evaluating surgical procedures, veterinarians may use statistical models to predict the likelihood of complications or postoperative outcomes.

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Quadratic equations is an equation that has a standard form of a·x² + b·x + c = 0

The correct values are presented as follows;

(a) If the pottery makes 5 bowls a week, the number of plates that can be made is 18 plates

(b) The maximum number bowls produced in a week is 15 Bowls

The reason the above values are correct are as follows:

The given relation between the number of bowls, B, and plates, P, that can be made in a week is presented as follows;

2·B² + 5·B + 25·P = 525

(a) Required: The number of plates that can be made if five (5) bowls are made each week

Solution:

To find out the number of plates that can be made, the given number of bowls (5) is placed in the equation as follows;

When B = 5, we get;

2 × 5² + 5 × 5 + 25·P = 525

25·P = 525 - (2 × 5² + 5 × 5) = 450

P = 450/25 = 18

P = 18

If the pottery makes 5 bowls a week, the number of plates that can be made, P = 18 plates

(b) Required: To find the maximum number of bowls that can be produced each week

Solution:

The given relation is rewritten as follows;

2·B² + 5·B + 25·P = 525

Given that the sum of the bowls B, produced and plates, P, produced is a constant, the maximum number of bowls is produced when the minimum number of plates are made

Therefore, when no plates are made, we get;

P = 0

2·B² + 5·B + 25×0 = 525

2·B² + 5·B = 525

2·B² + 5·B - 525 = 0

Factorizing with a graphing calculator, or by the quadratic formula, gives;

Calculator: (B - 15)·(2·B + 35) = 0

Quadratic formula: B = (-5 ± √(5² - 4 × 2 × (-525)))/(2 × 2)

∴ The maximum number bowls, B = 15 or -35/2

The positive value of B is used, therefore;

The maximum number bowls produced in a week = 15 Bowls

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Answer: the thermometer is precise, but not accurate. :)

Step-by-step explanation:

I just took the test on Apex and got it right, but to explain this answer:

the more places past the decimal a number has, the more precise it is. :)

31.08°F is precise because it’s got two places past the decimal but isn’t accurate because it’s not super close to 32.6°F :)

i hope that helped! and remember apex sucks:)

The thermometer is precise, but not accurate.

The degree of closeness of measurements of a quantity to its real value is the accuracy of a measuring system.

The degree to which repeated measurements under the same conditions produce the same findings is the precision of a measuring system, which is linked to reproducibility and repeatability.

If there is a systematic mistake in an experiment, increasing the sample size often improves precision but not accuracy.

Since the temperature of 32.6 °F is shown 31.08 °F which means the true value of the temperature is not shown. That means the value is not accurate.

But the value is calculated for the hundredth place which means the value is precise.

Hence, option C) is correct. That means the thermometer is precise but not accurate.

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The function that has the same minimum value as fx= 3x³ is f(x) = x + 3.

It should be noted that a function simply means a relation or expression that involves two or more variables.

In this case, the function that has the same minimum value as the expression of 3x³ is f = x + 3.

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Answer:b

Step-by-step explanation:

Answer:

SSS

Step-by-step explanation:

XS=SZ

WS=SY

WX=ZY

I hope this is useful.

The congruence theorem that can be used to prove △WXS ≅ △YZS is SSS. ; option A.

Congruence theorems are theorems which are used to prove congruency in triangles.

The congruence theorems include:

In the given triangle;

Therefore, the congruence theorem that can be used to prove △WXS ≅ △YZS is SSS.

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\((f-g)(-4)=f(-4)-g(-4)=[3(-4)^2 +5]-[-2(-4)+2]=\boxed{43}\)

Answer:

x = 10 yd

Explanation:

These triangles are based on proportions. 12 yd is proportional to 18 yd, and x yd to 15 yd. We want to find x. We'll use the rule of three to calculate the unknown number.

12/18 = x/15

x = (12 · 15)/18

x = 10 yd (10 yards from the hut to the gold coins)

Answer

The space given to plot the graph on you attached image does not have (16, 0), so, we need to obtain another point to plot this.

Using the equation of the line, y = -0.25x + 4, we obtain another point on the line

When x = 8

y = -0.25x + 4

y = -0.25 (8) + 4

y = -2 + 4 = 2

So, a third point on the line is (8, 2)

Using the points (0, 4) and (8, 2), you can plot this graph.

Mark the point (0, 4) on the graph first. This is simply the point on the vertical line where 4 is located.

Then, mark the point (8, 2) on the graph. You will trace the point on the x-axis (horizontal axis) where 8 is located upwards to meet the line of y = 2 on the y-axis (vertical axis).

You will then connect the two points marked. This is the graph required.

So, the graph will look like

Explanation

We are asked to plot the graph of y = -¼(x) + 4 or better written as

y = -0.25x + 4

To do this, we will use intercepts to get two points on the line and connect those two points to plot the graph

y = -0.25x + 4

When x = 0

y = -0.25x + 4

y = -0.25 (0) + 4

y = 0 + 4 = 4

First point on the line is (0, 4)

when y = 0

y = -0.25x + 4

0 = -0.25x + 4

0.25x = 4

Divide both sides by 0.25

(0.25x/0.25) = (4/0.25)

x = 16

Second point on the line is (16, 0)

So, connecting the two points (0, 4) and (16, 0).

The graph is shown under 'Answer'.

Hope this Helps!!!

\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)

Answer:

B (2.5, 0)

Step-by-step explanation:

2x - y = 5 (multiply all by 4)

8x- 4y = 20

-8x - 4y = - 20

eliminate the 4y

8x- 4y = 20

-8x - 4y = - 20

-------------------- –

16x = 40

x = 40/16 = 2.5

now we substitute x with 2.5

2x - y = 5

2(2.5) - y = 5

y = 0

Answer:

its B

Step-by-step explanation:

took the test

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps