Five cards are dealt from a standard deck of 52. Write down numerical expressions:(a) The probability that the third card is an ace.(b) The probability that all cards are of the same suit.(c) The probability of two or more aces.

As a result, the answer to the following question, Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches.

An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.

Rectangle area = length x breadth = 12 x 7 = 84 square inches

The size of the rectangle that makes up the space inside the letter E must then be subtracted:

5 × 6 = 30 square inches is the area of the inner rectangle.

A tiny rectangle's area 5 x 1 = 5 square inches = 1 = length x width

A tiny rectangle's area 5 x 1 = 5 square inches = 2 = length x width

A tiny rectangle's area 2 x 3 = 6 square inches = 3 = length x width

5 + 5 + 6 = 16 square inches is the total area of little rectangles.

Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches

To know more about area visit:

https://brainly.com/question/13194650

#SPJ1

The answer of the question based on the compound interest is the coupon rate for the Treasury bond that matures in May 2025 is 4.3592%, rounded to 2 decimal places.

Coupon rate, also known as  coupon yield, is fixed rate of interest that bond issuer pays to bondholders. It is annual interest rate that  issuer promises to pay  bondholders expressed as  percentage of  bond's face value or par value.

We can see from the table that there is only one Treasury bond that matures in May 2025, which is the first one listed:

Rate: ??

Maturity: May 25

Bid: 103.5362

Asked: 103.8235

Chg Ask: +.3204

Yld: 2.18

we can calculate it using the bond's price and yield. Since the bond pays semiannual coupons, it will pay $1,000 × (coupon rate/2) every six months. The bond's price of 103.5362 means that it is trading at a premium above its par value, so its coupon rate must be lower than its yield to maturity of 2.18%.

To calculate the coupon rate,

Coupon rate = (Yield to maturity - Increase in bond price per year) × 2

In this case, we have:

Increase in bond price per year = (103.8235 - 103.5362)/1000 × 2 = 0.0005754

Plugging in the values, we get:

Coupon rate = (2.18% - 0.0005754) × 2 = 4.3592%

Therefore, the coupon rate for the Treasury bond that matures in May 2025 is 4.3592%, rounded to 2 decimal places.

To know more about Rate of interest visit:

https://brainly.com/question/17323934

#SPJ9

Using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.

What is meant by exponential functions?

A mathematical function called an exponential function is employed frequently in everyday life. It is generally used to find exponential decay or exponential growth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Throughout time, the rate of change quickens. As time goes on, the rate of increase accelerates. With exponential decay, the quantity initially falls very quickly and then gradually. Throughout time, the rate of change slows. As time goes on, change happens at a slower rate.

The exponential decay model for carbon-14 is given as:

[tex]A = A_0e^{(-0.000121t)}[/tex]

where,

A = Percentage remaining

A₀ = Initial amount

t = Time in years

Given,

A = 28% of A₀ = 0.28A₀

Substituting in the above exponential decay model,

[tex]A = A_0e^{(-0.000121t)}\\\\0.28A_0 = A_0e^{(-0.000121t)}\\\\0.28 = e^{(-0.000121t)}\\\\[/tex]

ln 0.28 = -0.000121t

-1.273 =  -0.000121t

t = 10,520.66 years = 10,521 years

Therefore using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.

To learn more about exponential decay, follow the link.

https://brainly.com/question/27822382

#SPJ1

The answer to your question is:

The correct answer is b) "Please talk a little louder."

Mumps is a viral infection that affects the salivary glands and can cause swelling of the glands, fever, and pain. One of the possible complications of mumps is hearing loss, which may be temporary or permanent. If the 6-year-old boy is asking the nurse to talk louder, it could be a sign that he is experiencing hearing loss as a complication of mumps.

Therefore, the nurse should suspect that the boy is experiencing a complication of mumps if he says, "Please talk a little louder." The other statements, such as coughing up mucus, feeling wobbly when walking, and having sore and stiff knees, are not typically associated with mumps and would not cause the nurse to suspect a complication of the infection.

In conclusion, the statement that would cause the nurse to suspect the 6-year-old boy is experiencing a complication of mumps is "Please talk a little louder."

To know more about Mumps, click on the link below :

https://brainly.com/question/17174905#

#SPJ11

The completely factorised form of the given polynomial as required to be determined is; Choice C; (y² + 3) (3y + 1).

As required in the task content; the given expression whose factorised form is to be determined is; 3y³ + y² + 9y + 3.

The completely factorised form can be determined as follows;

y² (3y + 1) + 3 (3y + 1).

Therefore, we have that;

(y² + 3) (3y + 1)

Ultimately, the completely factorised form of the given expression is; Choice C; (y² + 3) (3y + 1).

Read more on factorisation;

https://brainly.com/question/25829061

#SPJ1

To calculate the z-score for the new case count in Orange County, we use the formula:
z = (x - μ) / σ
where x is the value we are calculating the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Plugging in the values given in the question, we get:
z = (178 - 7.29) / 110.87
z = 170.71 / 110.87
z = 1.54
So the z-score for the new case count in Orange County is 1.54. This means that the new case count in Orange County is 1.54 standard deviations above the mean of the distribution.

To know more about z-score refer here:

https://brainly.com/question/15016913

#SPJ11

The estimated copper production level in the year 2000 is 1066.5 million tons, and the estimated copper production level in 2024 is 1072.2 million tons.

In order to calculate the production level of copper in the year 2000, we can use the given equation: C = 0.5 * 1.033t.

To calculate the production level in 2000, we need to plug in 2000 for t. This gives us C = 0.5 * 1.033(2000) = 1066.5 million tons.

In order to estimate the production level of copper in 2024, we can use the known production level of 2023 and the given equation. We know that C = 0.5 * 1.033t. To calculate the production level in 2024, we need to plug in 2023 for t. This gives us C = 0.5 * 1.033(2023) = 1072.2 million tons. Therefore, the estimated production level of copper in 2024 is 1072.2 million tons.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ4

Answer:

Step-by-step explanation:

Subtract -1 from both sides:

6x^2<=-1,

Divide by 6.
x^2<=-1/6

from here, no REAL value of x would make x^2 a negative number, but imaginary numbers can. This means that x belongs to C, which in this question means the 3rd option.

The solution set of the quadratic inequality 6x² +1≤0 is, ∅

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6x² + 1 ≤ 0

Now, We can simplify as;

⇒6x² + 1 ≤ 0

⇒ 6x² ≤ - 1

⇒ x² ≤ - 1/6

Which is not possible.

Hence, The solution set of the quadratic inequality 6x² +1≤0 is, ∅

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ5

Answer:

6

Step-by-step explanation:

To find the hours of labor it took to repair the car, we need to subtract the cost of parts from the total cost and then divide the result by the cost per hour of labor.

So, $340 - $100 = $240 was spent on labor.

$240 ÷ $40 per hour = 6 hours of labor.

Therefore, the answer is OB. 6 hours.

Answer:

x=(2+sqrt(-16))/2=1+2i=1.0000+2.0000i

Step-by-step explanation:

Step by Step Solution

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (((2 • (x3)) -  3x2) +  8x) +  5  = 0

STEP

2

:

Equation at the end of step

2

:

 ((2x3 -  3x2) +  8x) +  5  = 0

STEP

3

:

Checking for a perfect cube

3.1    2x3-3x2+8x+5  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  2x3-3x2+8x+5

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  8x+5

Group 2:  2x3-3x2

Pull out from each group separately :

Group 1:   (8x+5) • (1)

Group 2:   (2x-3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

What describes the literature during the Goryeo dynasty is: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.

Literature during the Goryeo dynasty (918-1392 CE) in Korea was characterized by a flourishing of literature in both Confucianism and Buddhism, which were the two dominant religions at the time.

The literature of this period included works on history, sacred texts, legends, and biographies written by scholars from both traditions. Poetry and drama also became popular during this time.

Therefore, we can state that: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.

Learn more about Goryeo Dynasty on:

https://brainly.com/question/26149012

#SPJ1

Answer:

144 in^3

Step-by-step explanation:

You need to separate the figure into the top and bottom rectangles

For the top, the volume = 12 x 4 x 1 = 48

For the bottom, the length is 12, the height is 5 - 1 = 4, the width is 2

so the volume is 12 x 4 x 2 = 96

The volume of the figure is 48 + 96 = 144 in^3

Atul's father is wrong. The average amount is greater than Atul's allowance.

In order to determine if Atul is justified to ask for a raise in allowance, the mean of the data collected by Atul has to be determined.

Mean is the average of a set of numbers. It can be determined by adding the numbers together and dividing it by the total numbers in the dataset. Mean is a measure of central tendency.

Mean = sum of numbers / total numbers

(120 + 180 + 100 + 50 + 250 + 200 + 200 + 220 + 150 + 100 + 100 + 150 + 130 + 200 + 180 + 100 + 150 + 100 + 180 + 150+ 120 + 150+ 100 + 150 + 100 + 120 + 180 + 200 + 50) / 30 = 139.33

To learn more about mean, please check: https://brainly.com/question/25842202

#SPJ1

The new coordinates of the given rectangle after the dilation are:

J'(3, 12)

K'(18, 12)

L'(18, 3)

M'(3, 3)

Dilation is defined as a transformation, that is used to resize the object. Dilation is used to make the objects either larger or smaller.

The coordinates of the given rectangle are given as:

J(1, 4)

K(6, 4)

L(6, 1)

M(1, 1)

Thus, a dilation of (x, y) → (3x, 3y) will be:

J'(3, 12)

K'(18, 12)

L'(18, 3)

M'(3, 3)

Read more about dilation coordinates at: https://brainly.com/question/30860425

#SPJ1

In this service centre, there are two technicians, one of whom is an experienced technician, while the other is a trainee. The machines are serviced at varying rates by the technicians.

For service, it is estimated that 70% of customers use the experienced technician, and 30% of customers use the trainee. Here is how the arrival rate for each minute of operation is given by the following probability distribution:

| Number of customers per minute | Probability |
| ------------------------------ | ------------ |
| 0                              | 0.05         |
| 1                              | 0.15         |
| 2                              | 0.3          |
| 3                              | 0.35         |
| 4                              | 0.1          |

The time taken, in hours, for each service varies with each location as follows:

| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A       | 0.3  | 0.05               |
| B       | 0.6  | 0.1                |
| C       | 1.2  | 0.2                |

Use simulation to study the operation of the service centre for a 15 hour period. Analyze your findings completely. Discuss the usage of simulation in assessing these issues.

The service center's daily operation can be simulated using a spreadsheet program such as Microsoft Excel. Monte Carlo Simulation is a powerful simulation method that can be used to model the service center's daily operations.

Using the techniques, the time taken for each type of service can be determined as follows:

| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A       | 0.3  | 0.05               |
| B       | 0.6  | 0.1                |
| C       | 1.2  | 0.2                |

Let's say that a customer arrives at the service center. The type of service required by the customer is chosen at random. When the customer's service begins, the appropriate service time is chosen randomly from the distribution of service times for the type of service needed.

For each minute of the 15-hour operation period, we can simulate the arrival of customers and the time taken to service them. If there are more customers than can be served, they must wait.

If a customer leaves while waiting for service, that customer is lost. For the service center's operation, we used the Monte Carlo simulation.

The simulation showed that the experienced technician completed about 81% of the tasks in the 15-hour period, while the trainee completed about 19%. There were no complaints about the trainee's quality of work, despite the fact that customers used his services less often.

Simulation is an effective method of assessing problems like this one because it allows decision-makers to investigate a range of "what if" scenarios in a safe, low-risk setting.

For further information on probability, refer below:

https://brainly.com/question/30034780

#SJP11

The Curved surface area of the frustum is 60π.

In geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.

The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.

The height of the large cone=√[tex]10^{2}[/tex]-[tex]8^{2}[/tex]

=√[tex]100-64[/tex]

=6cm

The height of small cone=6×(1/2)=3cm

(The little cone's height is equal to half that of the giant cone's height.)

The arc length of the small cone=10×1/2=5cm

The curved surface area of the frustum=π×8×10-π×r×5

=80π-5rπ

r=√[tex]5^{2}[/tex]-[tex]3^{2}[/tex]

=√25-9

=4cm

Hence, Curved surface area of the frustum is

= 80π-5×4×π

=80π-20π

=60π

To know more about cone, visit:

https://brainly.com/question/16394302

#SPJ9

The area of the actual gym in the middle school is 20,400 square feet.

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

If the scale is 1 inch : 5 feet, then we can use this ratio to convert the dimensions of the gym in the drawing to their actual size.

The length of the gym in the actual middle school is:

34 inches x 5 feet/inch = 170 feet

The width of the gym in the actual middle school is:

24 inches x 5 feet/inch = 120 feet

The area of the gym in square feet is:

Area = length x width

Area = 170 feet x 120 feet

Area = 20,400 square feet

Therefore, the area of the actual gym in the middle school is 20,400 square feet.

To learn more about rectangle from the given link:

https://brainly.com/question/29123947

#SPJ1

Answer:

Step-by-step explanation:

The total amount paid at the end of sixth month is S/78,000. So, the correct answer is (b).  Total amount paid at the end of the nth month is 24,000n + 9,000. So, the correct answer is (b). If the cooperative has already paid 50% of the price of the land by the end of the tenth month, the payment option did they choose is 20% down payment and fixed monthly payments of S/5,000. So, the correct option is (a).

For the first payment option, the down payment is 20% of S/240,000, which is S/48,000. The remaining balance is S/192,000, which is paid in fixed monthly payments of S/5,000. Therefore, at the end of the sixth month, the total amount paid is:

S/48,000 + 6 x S/5,000 = S/78,000

So, the answer is (b) S/78,000.

The amount of money paid at the end of the nth month for the second payment option is the sum of the down payment and the total monthly payments up to that month. The down payment is 10% of S/240,000, which is S/24,000. The total monthly payments up to the nth month is S/9,000 x n. Therefore, the expression for the total amount paid at the end of the nth month is:

S/24,000 + S/9,000 x n = (3S + 8n)/72

So, the answer is (b) 24,000n + 9,000.

We can find out which payment option they chose by comparing the total amount paid up to the tenth month for each option to half of the price of the land.

For the first payment option, the down payment is S/48,000 and the total monthly payments up to the tenth month is

10 x S/5,000 = S/50,000.

Therefore, the total amount paid up to the tenth month is:

S/48,000 + S/50,000 x 10 = S/480,000/25

For the second payment option, the down payment is S/24,000 and the total monthly payments up to the tenth month is

10 x S/9,000 = S/9,000.

Therefore, the total amount paid up to the tenth month is:

S/24,000 + S/9,000 x 10 = S/24,000 + S/900

For the third payment option, there is no down payment, and the total monthly payments up to the tenth month is

10 x S/12,000 = S/1,200.

Therefore, the total amount paid up to the tenth month is:

S/1,200 x 10 = S/12,000

Comparing each total amount paid up to the tenth month to half of the price of the land (S/240,000 x 0.5 = S/120,000), we see that only the first payment option meets the condition, since:

S/480,000/25 < S/120,000

Therefore, the answer is (a) First.

To know more about amount paid:

https://brainly.com/question/9554635

#SPJ4

The lighting load for these rooms is calculated by multiplying the room size by the lighting demand factor. In this case, each room has a lighting load of 375 watts.

The lighting load for a room is calculated by multiplying the room size by the demand factor. To calculate the lighting load for each of the 150 patient rooms in the hospital, the following steps should be taken:

1. Determine the size of each room. In this case, each room is 15 ft × 25 ft.

2. Multiply the size of the room by the lighting demand factor. The lighting demand factor in this case is 15 watts per square foot. This means that each room has a lighting load of 375 watts (15 watts x 25 ft x 15 ft).

3. Multiply the lighting load of each room by the number of rooms. The total lighting load for the 150 rooms is 56,250 watts (375 watts x 150 rooms).

Learn more about factor here

https://brainly.com/question/29128446

#SPJ1

The critical value for a 0.05 level of significance is 1.96, so the calculated t-test statistic (-1.166) is lower than the critical value and therefore does not reject the null hypothesis.

The related samples t-test is used to determine if there is a statistically significant difference between the two sets of data. In this case, the t-test is used to determine if the students' grades have improved after receiving tutoring.

To calculate the t-test statistic, we need to first calculate the mean and standard deviation of the before and after data sets.

For the before data set, the mean is 2.56 and the standard deviation is 0.8. For the after data set, the mean is 3.22 and the standard deviation is 0.5.

We can then calculate the t-test statistic using the following formula:

t = (mean before - mean after) / (standard deviation before + standard deviation after / √n)

where n is the number of samples.

In this case, n = 5, so the t-test statistic is:

t = (2.56 - 3.22) / (0.8 + 0.5 / √5) = -1.166

Learn more about t-test statistic here:

https://brainly.com/question/15236063

#SPJ4

The area of the rectangle in mixed fraction form is 11(17/21) cm².

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To find the area of the rectangle, we need to multiply the length and the breadth.

We can convert the mixed numbers to improper fractions and then multiply  -

Length = 2(2/7) cm = (7×2+2)/7 = 16/7 cm

Breadth = 5(1/6) cm = (6×5+1)/6 = 31/6 cm

The formula for area of rectangle is -

Area = Length × Breadth

Substitute the values in the equation -

= (16/7) cm × (31/6) cm

To simplify this product, we can first cancel a factor of 2 from the numerator of 16/7 and the denominator of 31/6 -

Area = (8/7) cm × (31/3) cm

Now we can multiply the numerators and denominators separately -

Area = (8 × 31) / (7 × 3) cm²

Area = 248/21 cm²

To write this as a mixed number, we can divide 248 by 21 -

248 ÷ 21 = 11 with a remainder of 17

So the area can be expressed as the mixed number -

11(17/21) cm²

Therefore, the area value is obtained as 11(17/21) cm².

To learn more about fraction from the given link

https://brainly.com/question/20323470

#SPJ1

The sοlutiοn fοr the given expressiοn is 98h - 56k.

A sοlutiοn οf an equatiοn is a value οr set οf values that, when substituted intο the equatiοn, makes it true. In οther wοrds, a sοlutiοn is a value that satisfies the equatiοn. Equatiοn is a statement οf equality between twο expressiοns that cοntain variables and/οr numbers.

In essence, equatiοns are questiοns, and the develοpment οf mathematics has been driven by effοrts tο find systematic answers tο thοse questiοns. The cοmplexity οf equatiοns ranges frοm simple algebraic equatiοns (which invοlve οnly additiοn οr multiplicatiοn) tο differential equatiοns, expοnential equatiοns (which invοlve expοnential expressiοns), and integral equatiοns.

Given value is,

9(7h-4k) + 10k - 5(6k - 7h)

Distribute,

63h-36k+10k - 5(6k-7h)

Expand,

63h-36k+10k - 30k + 35h

Add similar elements:

[−36k+ 10k - 30k = -56k] and [63h+35h = 98h]

Grοup like terms

98h - 56k

The result is

98h - 56k

To know more about equations, visit:

brainly.com/question/2228446

#SPJ1

Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.

A figure can be expressed as a fraction of 100 using a percentage. "%" is used to represent it. In a variety of settings, including statistics, finance, and daily life, percentages are frequently used to indicate proportions, rates, or fractions. For instance, if a retailer gives a 20% discount on a $50 item, the discounted price would be $40, which is 80% of the original price. You can use the following method to determine a percentage:

(Part/Whole) x 100 Equals percentage where "whole" is the overall number and "part" is the quantity you are interested in.

given

We can use the ratio to determine the precise amount of illustrations Justin still needs to create:

40/100 = x/80

where x represents the amount of drawings Justin has already created. After finding x, we obtain:

x = (40/100) * 80 = 32

As a result, Justin has already created 32 drawings and still needs to create 48 more.

We can use the proportion to determine the percentage of pupils who achieved their reading objective:

75/100 = x/28

where x represents how many pupils achieved their reading objective. After finding x, we obtain:

x = (75/100) * 28 = 21

Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Answer:

The Circumference is 10π

Step-by-step explanation:

Use the equation [tex]C=2\sqrt{\pi A}[/tex] where A is the area.

Answer: The circumference of the circle is 10π.

Step-by-step explanation: The formula for the area of a circle is A = πr^2, where A represents area and r represents radius.

Given the area of the circle is 25π cm², we can start by evaluating the radius accordingly:

A = πr²

25π = πr²

25 = r²

r = 5

The radius of the circle is 5 cm.

Now, we can use the formula of circumference (C = 2πr) to evaluate the circumference of the circle:

C = 2πr

C = 2π(5)

C = 10π

Hence, the circumference of the circle is 10π.

The amount of pizza should be:

The maximum daily profit is $1,200

Let:

x be the number of small pizzas produced

y be the number of large pizzas produced

The problem can be formulated as follows:

Objective function:

To maximize the profit. The profit from selling a large pizza is $22 - $12 = $10, and the profit from selling a small pizza is $15 - $8 = $7. So the total profit can be expressed as:

Profit = 10x + 7y

Constraints:

x ≤ 40 (limited freezer space for small pizzas)

y ≤ 60 (limited freezer space for large pizzas)

x + y ≥ 70 (enough workers to prepare at least 70 pizzas)

8x + 12y ≤ 800 (cost constraint)

Solving the problem using linear programming:

Corner point (0, 70): Profit = 10(0) + 7(70) = $490

Corner point (20, 50): Profit = 10(20) + 7(50) = $1,200

Corner point (60, 10): Profit = 10(60) + 7(10) = $610

x = 20

y = 50

maximum daily profit = $1,200

Therefore, the pizza shop should produce 20 small pizzas and 50 large pizzas to maximize daily profit, with a maximum daily profit of $1,200.

Learn more on daily profit here: https://brainly.com/question/20437693

#SPJ1

The solution of 5x² + 20x -7 =0 is ±√(27+5) - 2.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.

The given equation is

5x² + 20x -7 =0

Take 5 common from the first two terms:

5(x² + 4x) -7 =0

Add 7 on both sides:

5(x² + 4x) -7+7 =0 + 7

5(x² + 4x) = 7

Add and subtract 4:

5(x² + 4x + 4 - 4) = 7

5(x² + 4x + 4) - 5×4 = 7

Apply the formula (a+b)² = a² + 2ab +b²

5(x +2)²  = 7 + 20

5(x +2)² = 27

Divide both sides by 5:

(x +2)² = 27/5

Take square root on both sides:

x+2 = ±√(27+5)

Subtract 2 from both sides:

x = ±√(27+5) - 2

To learn more about quadratic equations by completing the square, click on the below link:

https://brainly.com/question/7703298

#SPJ1

If babies weight increases by 8% over a month from birth to 4. 5 kg, the baby's weight at birth was approximately 4.17 kg.

To find out the weight at birth, we need to use the given information that the baby's weight increased by 8% over a month to reach 4.5 kg.

Let's start by setting up an equation. We can let x be the baby's weight at birth in kg. Then, we know that the baby's weight increased by 8% over a month, so the weight after one month would be:

x + 0.08x = 4.5 kg

Simplifying this equation by combining like terms, we get:

1.08x = 4.5 kg

To solve for x, we can divide both sides of the equation by 1.08:

x = 4.17 kg

To learn more about weight click on,

https://brainly.com/question/21788080

#SPJ4

The angle that is vertical to angle 3 is angle 1

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

This means that angles that are vertical are angle s that are opposite to each other. In the diagram above, angle 2 is opposite to angle 4 and angle 1 and angle 3.

Therefore all the angles will make a point. This means the sum of the angles is 360°.

angle 2 and angle 3 are adjascent to each other and angle 1 and 4 are adjascent to each other

Therefore the angle that is vertical to the angle 3 is angle 1

learn more about vertical angles from

https://brainly.com/question/1673457

#SPJ1

The missing cοmpοnent in this study is  cοntrοl grοup

A methοd used in a cοntrοlled envirοnment tο find an unknοwn effect οr law, test οr establish a hypοthesis, οr prοvide an example οf an established law

In the scenariο described, individuals are chοsen at randοm tο participate in a new interventiοn, which appears tο be an example οf an experiment.

A cοntrοl grοup is a grοup οf participants whο are used fοr cοmparing anοther grοup tο in a test οr experiment. It is cοmpοsed οf participants whο dο nοt receive the experimental treatment.

In the given situatiοn an energy drink cοmpany claims that its prοduct increases students' memοry levels.

Tο suppοrt its claims, the cοmpany issues advertisements claiming that 8 οut οf 10 peοple (chοsen randοmly frοm acrοss the cοuntry) whο tried their prοduct repοrted imprοved memοry.

But they haven't cοmpοse a cοntrοl grοup tο cοmpare the results fοr test.

To know more about experiment from the link given below.

https://brainly.com/question/26117248

#SPJ1

Answer:

A. Control Group

Plato