Given f(x)=x^2+kx-19 and the remainder when f(x)is divided by x-7 is −5, then what is the value of k

The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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Answer:

-9/8

Step-by-step explanation:

3x + 9 + 4x + x

Collect like terms

3x + 4x + x = -9

8x = -9

Divide both sides by 8

8x/8 = -9/8

x = -9/8

The limits of accuracy for the area of triangle ABC are 24.03 cm² and 47.15 cm².

To calculate the limits of accuracy for the area of triangle ABC, we first need to calculate the maximum and minimum possible values for the height of the triangle.

Using the sine rule, we can find the length of AC:

sin(37°)/7 = sin(53°)/AC

AC ≈ 10.55 cm

Now, we can calculate the maximum and minimum possible heights of the triangle

Maximum height: h = AC = 10.55 cm

Minimum height: h = sin(37°) x 9 ≈ 5.34 cm

Therefore, the limits of accuracy for the area of triangle ABC are:

Maximum possible area: (1/2) x 9 x 10.55 ≈ 47.15 cm²

Minimum possible area: (1/2) x 9 x 5.34 ≈ 24.03 cm²

So, the area of the triangle can be said to be between approximately 24.03 cm² and 47.15 cm².

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--"The given question is incomplete, the complete question is given below:

in triangle ABC, AB= 9cm, BC=7cm and ∠ABC = 37°. All the measurements are given to the nearest unit. Calculate the limits of accuracy for the area of the triangle"--

Answer:

Step-by-step explanation:

39

Answer:

39 is the answer you are looking for

To find the correct equations for the missing boxes, we need more information about the relationships between the different activities in Jake's Gems. However, based on the given context, we can make some assumptions and suggest potential equations:

Mining and Cutting activities produce diamonds, rubies, and other gems. Let's assume that the production of each gem type is represented by a variable: D (diamonds), R (rubies), and G (other gems).

Maintenance supports the Mining and Cutting activities. We can assume that the maintenance effort required for each activity is represented by the variable M (maintenance).Since the question mentions five missing boxes, we can suggest additional equations to represent relationships between these variables, such as:

Mining + Cutting = D + R + G (the sum of all gem types produced equals the total production from Mining and Cutting activities).

Maintenance = M (maintenance effort required).

The relationships between these variables might include equations like D = f(M), R = g(M), G = h(M), where f, g, and h represent some functions or formulas that relate gem production to maintenance effort.

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Answer:

\(y=25x\)

Step-by-step explanation:

If Bella types 50 words in 2 minutes, we can divide 50 by 2 to see how many words she types in 1 minute.

\(50/2=25\)

So, Bella types 25 words per minute. When she first began writing her essay, she did not have words to start with, so there is no y-intercept (\(b\)).

Therefore, the equation that represents this relation is \(y=25x\).

Solving the equation

We can divide 400 by 25 to determine how many minutes it would take her to finish her essay.

\(\frac{400}{25} =16\)

Therefore, it will take her 16 minutes to complete her essay.

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Answer:

the first option

Step-by-step explanation:

Answer:

John Marston

Step-by-step explanation:

Answer:

Arthur Morgan

Step-by-step explanation:

He is simply Amazing

After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

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The complete question is given in the image.

Answer:

\(2\frac{3}{4}\)

Step-by-step explanation:

We have to subtract the weight of the cat from the weight of the dog.

\(8\frac{1}{4} -5\frac{1}{2}\)

The first issue here is that there is not a common denominator. I'm going to multiply that 1/2 by 2 to make it 2/4. The 5 does NOT change.

\(8\frac{1}{4} -5\frac{2}{4}\)

Subtract the whole numbers first.

\(8\frac{1}{4} -5\frac{2}{4} = 3\frac{1}{4} -\frac{2}{4}\)

Then, we'll convert the first term to an improper fraction. We can do that by multiplying the whole number by the denominator and adding that number to the numerator.

\(3\frac{1}{4} -\frac{2}{4} ==> \frac{13}{4} - \frac{2}{4}\)

Solve.

\(\frac{13}{4} -\frac{2}{4} = \frac{11}{4}\)

Then, convert to a mixed number by dividing 11 by 4 and leaving the remainder in the numerator and putting the quotient in front as the whole number.

\(\frac{11}{4} ==> 2\frac{3}{4}\)

So, the answer is \(2\frac{3}{4}\)

2 3/4

Steps

8 1/4 - 5 1/2

a. Find Common Denominator

8 1/4 - 5 2/4

b. Make Improper Fractions

8 × 4 + 1 = 33

33/4

5 × 4 + 2

22/4

c. Subtract

33/4 - 22/4 = 11/4

d. Simplify

11/4 = 2 3/4

e. Answer

Therefore, Priya's dog is 2 3/4 pounds heavier than the cat.

The cost of 10 strands of lights operating them for 30 days depends on a number of factors such as the type of lights, the wattage of the bulbs, and the cost of electricity per kilowatt-hour. To calculate the cost of electricity.

the formula is used:

Cost = Power × Time × Cost per kWh

Where,
Power is the wattage of the bulb
Time is the duration of use in hours
Cost per kWh is the cost of electricity per kilowatt-hour

Assuming that each strand of light has 100 bulbs, and each bulb has a wattage of 0.5 watts, then the total wattage of 10 strands of lights would be:

Total wattage = 100 bulbs × 0.5 watts/bulb × 10 strands
= 500 watts

Now, assuming that the cost of electricity per kilowatt-hour is $0.15, the cost of operating 10 strands of lights for 30 days would be:

Cost = Power × Time × Cost per kWh
= 500 watts × (30 days × 24 hours/day) × $0.15/kWh
= 500 watts × 720 hours × $0.15/kWh
= $54

Therefore, the total cost of operating 10 strands of lights for 30 days would be $54.

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Answer:

Step-by-step explanation:

Y equals mx plus b

Norma still has 13/3 cups of lemonade left to sell

Norma made 68/12 cups of fresh lemonade.

She sold 4/3 cups of lemonade.

To calculate the remaining lemonade, we subtract the sold amount from the total:

Remaining lemonade = Total lemonade - Sold lemonade

Total lemonade = 68/12 cups Sold lemonade = 4/3 cups

Remaining lemonade = (68/12) - (4/3)

To subtract fractions, we need a common denominator. In this case, the least common multiple of 12 and 3 is 12.

Remaining lemonade = (68/12) - (16/12)

Now, we can subtract the fractions:

Remaining lemonade = (68 - 16) / 12 Remaining lemonade = 52/12

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:

Remaining lemonade = (52/4) / (12/4) Remaining lemonade = 13/3

Therefore, Norma still has 13/3 cups of lemonade left to sell, which is equivalent to 4 and 1/3 cups of lemonade.

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Answer:

the answer is ieff = 2% - 3.24%

ieff = - 1.24% = -0.0124

Therefore the money left after 1 year would be:

F = 44,000 * (1 – 0.0124)

F = 43,454.4

So the amount of money lost is:

lost = 44,000 - 43,454.4

lost = $545.6

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Step-by-step explanation:

a. The minimum sample size needed is 601.

b. The minimum sample size needed using a prior study is 304.

c. The difference between the results from parts (b) and (a) shows that a preliminary estimation of the population proportion can lower the necessary minimum sample size.

The signed, fractional number of standard deviations above the mean value that an event is above is expressed by the dimensionless variable known as the z-score. Among other names, it is also referred to as the normal score, z-value, and standard score. Z-scores are indicative of values that are higher than the mean and lower than the mean.

(a) To find the minimum sample size needed assuming that no prior information is available, we can use the formula:

n = (Zα/2)² *\(\hat p \hat q\)/ E²

where Zα/2 is the z-score corresponding to the desired level of confidence (90% confidence corresponds to a z-score of 1.645), \(\hat p\) is the sample proportion (unknown), \(\hat q = 1 - \hat p\), and E is the maximum error of estimation (2% of the true proportion, or 0.02).

Plugging in the values, we get:

n = (1.645)² * 0.5*0.5 / 0.02² ≈ 601

Consequently, 601 is the required minimum sample size.

(b) To find the minimum sample size needed using a prior study that found that 42% of the respondents said they think Congress is doing a good or excellent job, we can use the formula:

n = (Zα/2)² * \(\hat p \hat q\) / E²

where now we have a preliminary estimate of the population proportion, \(\hat p = 0.42, and \hat q = 1 - \hat p.\)

Plugging in the values, we get:

n = (1.645)² * 0.42*0.58 / 0.02² ≈ 304

Therefore, the minimum sample size needed using a prior study is 304.

(c) The result from part (b) is smaller than the result from part (a), indicating that having a preliminary estimate of the population proportion can reduce the minimum sample size needed. This is because a preliminary estimate can provide a starting point for the sample size calculation, and reduce the variability of the sampling distribution.

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The final cost of the CD after the discount and sales tax is $12.26.

The cost of the CD after the discount and sales tax can be calculated as follows: Step 1: Find the discount amount 5% of $12 is:(5/100) x $12 = $0.60The discount is $0.60.Step 2: Find the sale price The sale price of the CD is: Original price - Discount= $12 - $0.60= $11.40Step 3: Find the sales tax amount 7.5% of $11.40 is:(7.5/100) x $11.40 = $0.855The sales tax is $0.855.Step 4: Find the final cost

The final cost of the CD is: Sale price + Sales tax= $11.40 + $0.855= $12.255.The final cost of the CD after the discount and sales tax is $12.26.

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Based on the given parameters, the value of x such that the lines are parallel is 20

Parallel lines are lines that extend indefinitely and do not meet

The given parameter is the lines in the figure

From the figure, we have the following angles:

3x + 20 and 2x + 40

The angles are corresponding angles

Corresponding angles are congruent

So, we have

3x + 20 = 2x + 40

Collect the like terms

3x - 2x = 40 - 20

Evaluate the like terms

x = 20

Hence, the value of x such that the lines are parallel is 20

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Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.

A fractional value is a value that represents a portion or part of the total value.

Fractional values can be depicted as proper, improper, or complex fractions.  They can also be depicted as decimals or percentages.

The remaining quantity of the shell pile = ³/₄

The quantity sorted by Terrence = ⁴/₆

The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%

Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.

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We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

To solve the equation sin2x + cosx = 0 for x in the interval [0, π], we can use trigonometric identities and algebraic manipulation.

First, we can rewrite sin2x as 2sinx*cosx using the double-angle formula for sine: 2sinx*cosx + cosx = 0. Now, we can factor out cosx: cosx(2sinx + 1) = 0. To find the solutions, we set each factor equal to zero: cosx = 0 --> x = π/2, 3π/2 (since the interval is [0, π]), 2sinx + 1 = 0 --> sinx = -1/2. To solve sinx = -1/2, we refer to the unit circle or trigonometric table. We find that sinx = -1/2 for x = 7π/6 and x = 11π/6.

Therefore, the solutions to the equation sin2x + cosx = 0 in the interval [0, π] are: x = π/2, 3π/2, 7π/6, and 11π/6.

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The raster data model is commonly used to represent field features, but it is not suitable for representing point, line, and polygon features.

The raster data model is a grid-based representation where each cell or pixel contains a value representing a specific attribute or characteristic. It is well-suited for representing continuous spatial phenomena such as elevation, temperature, or vegetation density. Raster data is organized into a regular grid structure, with each cell having a consistent size and shape.

However, the raster data model has limitations when it comes to representing discrete features like points, lines, and polygons. Since raster data is based on a grid, it cannot precisely represent the exact shape and location of these features. Instead, they are approximated by the cells that cover their extent.

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The magnitude of the electric force upon an electron at point B is 8.16 x 10^-20 N, and it would accelerate in the direction opposite to the electric field, or -7.

The upon an electron at point B can be calculated using the formula F = qE, where F is the force, q is the charge of the electron, and E is the electric field magnitude. The charge of an electron is 1.6 x 10^-19 C, and the electric field magnitude at point B is 0.51 V/m. Therefore, the magnitude of the electric force is:

F = (1.6 x 10^-19 C) (0.51 V/m) = 8.16 x 10^-20 N

To determine the direction in which the electron would accelerate at point B, we need to consider the direction of the electric field. The electric field direction at point B is not given in the table, but we can assume that it is the same as the direction at point A, which is 7.

Therefore, the electron would accelerate in the direction opposite to the electric field, or -7.

The vector indicating the direction in which the electron would accelerate at point B can be drawn as follows:

<--- (electron)

In conclusion, the magnitude of the electric force is 8.16 x 10^-20 N, and it would accelerate in the direction opposite to the electric field, or -7.

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Answer:

Classify the sequence {1, 6, 11, 16, 21, …}.

The pattern is +5:

1 + 5 = 6

6 + 5 = 11

11 + 5 = 16

16 + 5 = 21

21 + 5 = 26

And so on

Step-by-step explanation:

You're welcome

Answer: 4 cubic inches.

Step-by-step explanation: since the height of the water bottle is 16, and a radius of 4 inches, 4x4=16, the volume in cubic inches is 4.

TIP: you can also divide 16 by 4.

The cost to pay for the gas if this car made a trip of 866 miles cost is $53.31.

A car averages 32 mpg and gas costs $1.97 per gallon.

By unitary method for 866 miles, average would be,

= 866/32

= 27.0625 miles per gallon

and the cost to pay for the gas if this car made a trip of 866 miles would be,

= 27.0625 × $1.97

= $53.31

Therefore, the cost to pay for the gas if this car made a trip of 866 miles cost is $53.31.

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Answer:

For a polynomial of the form ax2+bx+cax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅2=6a⋅c=3⋅2=6 and whose sum is b=5b=5.

Answer:

Step-by-step explanation: