. Solve for x: log₂ (x+4) + log₂ (x + 3) = 1. Pleasee

Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Step-by-step explanation:

First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".

We can set up the following equation: 3V + 4T = 85

Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.

We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42

Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.

We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.

For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.

If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15

Since V + T = 25, this means that T = 25 - 15 = 10

Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Answer:

1/64

Step-by-step explanation:

1/8 x 1/8 = 1/64

The number of boxes of sugar that Alonso can buy are 4.5 boxes.

Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.

The money remaining after buying 12 eggs : {r} = $(55 -2.75).

Cost of one box of sugar = $11.5

The number of boxes that he can buy are -

n = (55 - 2.75)/11.5

n = 4.5 boxes {approx.}

Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.

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The force on the object is 40N

Force can be described as the influence that can change the motion of an object.

It is seen as an external agent having the capability of changing a body's state of motion or rest.

It causes b in velocity of an object with mass , that is,  to accelerate. Force can also be described as either a push or a pull.

It is described as a vector quantity, that is, it has both magnitude and direction.

The formula for determining force is given as;

F = ma

Where;

Substitute the values

F = 10(4)

F = 40N

Hence, the value is 40N

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The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth

Multiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product

Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures

4 1/10 * -4 * 5/10

solving the equation

= 4 1/10 * -4 * 5/10

= 41/10 * -4 * 5/10

= -41/5

= -8 1/5

The product of the multiplication is negative 8 and one fifth

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We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Answer:

Step-by-step explanation:

[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]

The solution does not exist because all numbers squared are greater than zero.

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.

Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.

Given:

The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)

Angle of rotation = 90° about the origin

According to the question, let's take our start point as A(x, y)

So, A( x, y) will lie in the first quadrant.

After 90° rotation about the origin A' will lies in fourth quadrant.

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

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The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:

Cumulative probability is equal to (number of events * e)/(average number of events per time period).

(Number of events / (-average number of events per time period)!)

In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:

Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.

That amounts to:

Probability total = 1 + 0.05 + 0.0025

which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.

yes, z can lie between x and y but z can also lie on another side of x in Number lines.

With an example, define number line?

Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.

                  A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.

What does the math number line mean?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.

                               How a number is used—for example, to plot a point—depends on the question that goes with it.

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Answer:The Flemish giant rabbit weighs 32 pounds.

Step-by-step explanation:

A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours

Given,

Chance Product is designed to function for 10,000 hours

of failure is 3%

To find,

Average number of failures per hour

MTTF

Solution,

Average number of failures per hour = Chance of failure/Total hours of function

= 3%/10000

= 0.03/10000

= 0.000003

MTTF = 1/Average number of failures per hour

= 1/0.000003

= 333,333 hours

The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.

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Net payout will you be promised in a fair betting game in case your bet works out is $0 .

Given :

browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .

P ( browns ) = 60 / 100 = 0.60

P ( steelers ) = 40 / 100 = 0.40

Net payout = Number of wins * 10 - Number of loses * 10

= 1 * 10 - 1 * 10

= 10  - 10

= $0.

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The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The inequalities are,

2( x +6 ) > -6( x +1) +2

2x + 12 > -6x - 6 + 2

2x + 6x > -12 - 6 +2

8x > -16

x > -2

-3x - 1 ≥ 20

-3x ≥ 21

x ≥ -7

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Dependent variable: t (total cost of the pizza)

Independent variable: x (number of extra toppings)

Equation: t = 10.50 + 1.50x

To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:

t = 10.50 + 1.50(3)

t = 10.50 + 4.50

t = 15.00

So the total cost of the pizza with 3 extra toppings is $15.00.

What is Dependent Variables?

The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.

What is Independent Variables?

Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.

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Answer:

5832

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

we use the y2-y1/x2-x1 fomrula to find slope

14-8/7-10

6/-3

-2 is the slope

hopes this helps

The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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Answer:

What is 213 divided? 2 I think

Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones

We may calculate our answer using fractions and the fact that the base is 18.3 feet.

The components of a whole or group of items are represented by fractions. A fraction consists of two components.

The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

There are three different methods to express a fraction: as a fraction, as a percentage, or as a decimal. Let's examine each of the three representational styles.

According to our question-

The patio is 280 square feet in size. locate the base.

Height = 5x Area = 280 feet square

Base = 6x

The parallelogram A's area can be expressed mathematically as;

Base + height equals area.

A = b×h

the values of area, base, and height are substituted.

280 = 5x × 6x = 30x^2 \sx^2 = 280/30 \sx = √(280/30)

Given that the base is 6x,

swapping out x's value.

Base = 6x = 6(√(280/30))

Base=18.3 feet

18.3 ft tall is the base

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Answer:

At short 18.7 ft is the answer

Answer:

Below

Step-by-step explanation:

To complete the square, the coefficient of x^2 must be 1  ( it is already)

   then take 1/2 of the x coefficient  .... 1/2.... square it and add it to both sides of the equation

   x^2 + x + 1/4   + 9   = 1/4

 then you can reduce this to

   ( x+ 1/2)^2  + 9 = 1/4   for further 'solving'

The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

42 48 52 54 59 61 61 64 65 67 68 70 72 75 80

The given set of numbers is in ascending order.

There are 15 numbers.

The middle number will be the 8th number.

8th number = 64

Thus,

The median is 64.

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Answer:

Step-by-step explanation:

Answer:

-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

5.21 x 10^19 + 3.149 x 10^17

10^17(5.21 x 10^2 + 3.149)

10^17(521 + 3.149)

10^17(524.149)

5.24149 x 10^17 x 10^2

5.24149 x 10^(17+2)

5.24149 x 10^19

Answer: b. 5.24149 × 1019

Step-by-step explanation: I took the test

The perimeter of the object is the sum of the lengths of all the sides

which is 302 units.

Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.

In the case of a circle, we call it perimeter circumference it is the distance around the circle.

Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and

HG = 37.

Now the perimeter of this figure is the sum of the lengths of all the sides which is,

= (EF + FD + ED + IG + HG).

= (71 + 80 + 74 + 40 + 37).

= 302 units.

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The approximate mean and standard deviation of the number of chips meeting specifications are: μ = 16.2; σ = 1.273

In this question, we have been given a factory makes silicon chips for use in computers. it is known that about 90% of the chips meet specifications. every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded.

we need to find  the approximate mean and standard deviation of the number of chips meeting specifications

Since 90% meet specifications we can say p = 0.9

So, q = 1 - p

q = 1 - 0.9

q = 0.1

here,  a sample size is n = 18

So, the mean would be,

μ = np

μ = 18 * 0.9

μ = 16.2

And the standard deviation would be,

σ = √npq

σ = √(18 * 0.9 * 0.1)

σ = 1.273

Therefore, the mean (μ) = 16.2 and the standard deviation (σ) = 1.273

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Answer:

(A) 19 times, 16 people.

Step-by-step explanation:

There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.

The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.

Since the Caterpillar cannot run a fraction of a time, it must run 19 times.

There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.

Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.

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