BIRDHOUSES Ebony can build 0.7 birdhouse in 1 day. How many birdhouses can she build in 10 weeks?

The price of each bottle of juice is $1.03

What is an equation?

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let 'x' be the price of each bottle of juice. Then,

According to the question,

2.36 + 4x = 6.48

or, 4x = 6.48 - 2.36

or, 4x = 4.12

or, x = 4.12/4

or, x = 1.03

Hence, the price of each bottle of juice is $1.03

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Answer:

53 candy

Step-by-step explanation:

Answer:

blip

Step-by-step explanation:

blipgg

−32i is the answer if you use DeMoivre's theorem to find (1−i)^10.

A formula for determining the powers of complex numbers is provided by De Moivre's theorem. It might be easier to comprehend de Moivre's theorem if we first look at what happens when we multiply a complex number by itself. This illustrates how the argument is multiplied by two and the absolute value is squared when squaring a complex number.

One of the most important and useful theorems in the study of complex numbers is DeMoivre's Theorem, which combines trigonometry with complex numbers. It's also helpful to find relationships between trigonometric functions at different angles. The name of the theorem pays homage to the well-known mathematician De Moivre, who made several contributions to mathematics, notably in the areas of probability theory and algebra. Attached below is the answer.

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Answer:

All real numbers  are solutions

Step-by-step explanation:

Open the bracket

4(2x+3)=2(4x+6)

8x +12=8x +12

8X-8X=12- 12

=0

The equation is an identity hence, all real numbers are solutions(1,2,3,4 etc)

The equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.

Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

The definition of linear equations, the standard form for linear equations involving one variable, two variables, or three variables, and examples of each will all be covered in detail in this article.

Find the value of the variable that causes the equation to be true in order to solve linear equations.

Utilize the inverse of the variable's multiplier and divide or multiply both sides by it.

To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.

So, we have the pair of linear equations:

x – y = 8 and 3x – 3y = 16

(a1/a2) = 1/3

(b1/b2) = -1/-3 = 1/3

(c1/c2) = 8/16 = 1/2

Since, we know that (a1/a2) = (b1/b2) ≠ (c1/c2).

The equations have no solutions and run parallel to one another. The pair of linear equations is hence incoherent.

Therefore, the equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.

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Complete question:

Find out whether the following pairs of linear equations x – y = 8 and 3x – 3y = 16 are consistent/inconsistent.

here's two, I used mathday but day with a w

Step-by-step explanation:

good website for it and it gives good explanation! Gl

If abc is 1 degree and 25', the angle ACD is 178° 35'.

An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are termed dihedral angles. An angle is generated when two straight lines or rays meet at a shared terminus. The common point of contact is called the vertex of an angle.

Here,

∠ACB and ∠ACD are supplementary, so they add up to 180°.

First, convert to degrees (there are 60 minutes in a degree).

∠ACB = 1°25' = 1° + (25/60)° = 1.4167°

Now find the supplementary:

∠ACD = 180° − 1.4167°

∠ACD = 178.5833°

∠ACD = 178° 35'

The value of angle ACD is 178° 35' if abc is 1 degree and 25' .

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The length of the Antenna will be;

⇒ h = 18 meters

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Tyler is 1.8 meters and his shadow is 6 meters.

And, Tyler is standing 54 meters from the antenna.

Now,

Since, Tyler is 1.8 meters and his shadow is 6 meters.

And, Tyler is standing 54 meters from the antenna.

Let the length of the Antenna = x

Hence, We get by definition of proportional, we get;

⇒ 1.8 / 6 = h / (54 + 6)

⇒ 0.3 = h / 60

⇒ h = 0.3 × 60

⇒ h = 18 meters

Thus, The length of the Antenna will be;

⇒ h = 18 meters

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In percent, the fraction [tex]\frac{1}{9}\\\\[/tex] can be calculated as 11.11%.

A percentage is a common way to represent statistical data, and it is usually used to indicate one-hundredth, with the symbol "%." To calculate the percentage, it is given by:

Percentage (%) = value ÷ total value multiplied by 100%

In conclusion, the percentage of a fraction [tex]\frac{1}{9}\\\\[/tex] is 11.11%.

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The chi-square goodness-of-fit test is a statistical test that is used to determine whether a sample comes from a population with a specific distribution. There are a few conditions that must be met in order to use this test:

1. The data must be collected from a random sample. This ensures that the sample is representative of the population, which is necessary for the test to be valid.

2. The data must be categorical. This means that the observations must fall into distinct categories, rather than being continuous or ordinal.

3. The expected frequencies for each category should be at least 5. This ensures that the chi-square test statistic is approximately normally distributed, which is necessary for the test to be valid.

4. The data must be independent. This means that the outcome of one observation should not influence the outcome of another observation.

If these conditions are not met, the chi-square goodness-of-fit test may not be appropriate. In such cases, it may be necessary to use a different statistical test.

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If she moves at a speed of 1.33 miles per minute while walking 4 miles in 3 minutes, she can cover 20 miles in 15 minutes.

A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

In 3 minutes, she walk 4 miles,

speed=distance/time

=4/3 miles/minute

distance=speed*time

=4/3*15

=20 miles

She can walk 20 miles in 15 minutes if she walks 4 miles in 3 minutes with a speed of 1.33 miles/minute.

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Answer:

21 sq. meters

Step-by-step explanation:

you just need to multiply the width and the height, so 3x7.

3x7=21

Answer: 21m^2

Step-by-step explanation:

The equation finds the area of a rectangle is

Area= Width times Height

So take 7 times 3 = 21 m^2

An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.

Step 1: Arrange the data in the worksheet's columns and rows.

Step 2: Choose the information.

Step 3: Click the Combo chart icon on the Ribbon under the Charts group on the INSERT tab.

Step 4: Click each icon with your mouse.

step 5 Double-click the chart type that suits your data.

A combo chart combines two column charts, two line graphs, or a column chart and a line graph into one visual representation.

An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.

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10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

percentage, a relative value indicating hundredth parts of any quantity.

The formula for quarterly compound interest formula:

[tex]A=P(1+\frac{r}{4} )^{4t}[/tex]

P is the principle amount

t is time

r is rate of interest

A is final amount

[tex]1750=1000(1+\frac{0.0575}{4} )^{4t}[/tex]

[tex]1750=1000(1+0.0144)^{4t}[/tex]

[tex]1750=1000(1.0144)^{4t}[/tex]

Divide both sides by 1000

[tex]1.75=1.0144^{4t}[/tex]

Take log on both sides

log1.75=4tlog1.0144

0.243=4t(0.006)

0.243=0.024t

Divide both sides by 0.024

t=10.12

t=10 years

Hence, 10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

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The values that make v ≥ 1 inequality true are 2, 3, 4, 5....

What is inequality in mathematics?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The inequality is given as:

v ≥ -1

The values of c for which the given inequality → v ≥ -1 is true will belong to the set (say A) -

A = [-1, - ∞)

Therefore, we have to select all numbers which fall in this set. The numbers are

-1, 0, 1, 2, 3,....

Rewrite properly as:

v ≥ 1

The above means that the true values of v are values greater than 1.

Hence, the values that make v  ≥ 1 inequality true are -1, 0, 1 , 2, 3, 4, 5....

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The partial derivative dy/dx at x = e is given as follows:

[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]

The function in this problem is defined as follows:

y = tan(u).

The function y is a function of the variable u, which is a function of the variable v, which is a function of variable x, then the function of variable x can be written as follows:

[tex]y = \tan{\left(\ln{x} - \frac{1}{\ln{x}}\right)}[/tex]

Then, applying the chain rule, the derivative is the derivative of the outer tangent function multiplied by the derivative of the inner ln function.

The inner function is of:

[tex]\ln{x} - \frac{1}{\ln{x}}[/tex]

Which has a derivative of:

[tex]\frac{1}{x} + \frac{1}{x\ln^2{x}}[/tex]

The outer tangent function has a derivative of:

-sec²(x).

Then the complete derivative is of:

[tex]\frac{dy}{dx} = -\sec^2{\left(\ln{x} - \frac{1}{\ln{x}}\right)} \times \left(\frac{1}{x} + \frac{1}{x\ln^2{x}}\right)[/tex]

At x = e, the numeric value of the derivative is given as follows:

[tex]\frac{dy}{dx}(e) = -\sec^2{0} \times \frac{2}{e}[/tex]

[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]

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The isotopes in the set I are [tex]^{14} _{7} B[/tex] and [tex]^{15} _{7} C[/tex] and set II are [tex]^{20} _{10} E, ^{21} _{10}F[/tex] and [tex]^{22} _{10} G[/tex].

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

Isotopes are elements with the same atomic number but different mass.

In this case, the elements in set I- B and C has the same atomic number 7 but had different mass numbers and the elements in set II- E, F and G had the same atomic number 10 and different mass numbers, therefore they are known as isotopes.

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The equation which represent the proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

y = bx

Where,

b = constant

If y = $6 and x = 2 pairs

y = bx

6 = b × 2

6 = 2b

divide both sides by 2

b = 6/2

b = 3

In conclusion, the proportional relationship between number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

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The height of the trapezoid is 5mm.

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is referred to as a trapezium in British and other varieties of English.

In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases. If the remaining two sides are parallel, the trapezoid is a parallelogram and has two pairs of bases; if not, they are referred to as the legs (or lateral sides). A scalene trapezoid is a trapezoid without equal-sized sides.

Given: Area of trapezoid = [tex]35mm^{2}[/tex]

We know, area of trapezoid = [tex]\frac{(a+b)}{2} .h[/tex]

⇒ [tex]\frac{(8+6)}{2} .h=35[/tex]

⇒ [tex]7h=35[/tex]

⇒ [tex]h=5mm[/tex]

Hence, the height of the trapezoid is 5mm.

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Answer:

x<5

Step-by-step explanation:

5(2x-3) < 35

_____ ___

5 5

2x-3<7

2x<10

_ _

2x 2x

x < 5

Answer:

B. Since [tex]\triangle ABC \cong \triangle DEF[/tex] by SSS and [tex]\triangle DEF \cong \triangle GHJ[/tex] by SAS, [tex]\triangle ABC \cong \triangle GHJ[/tex] by the Transitive Property of Congruence.

The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS

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

Triangles = ABC, DEF and GHJ

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark

AC and GJ

CB and JH

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following angles must also be congruent

AB must be congruent to GH

Hence, the congruent statement on the congruency of the triangles is (d)

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It is proportional because all y over x ratios are equivalent to one-third. I.e., the proportionality constant of the given table is k = 1/3.

The proportionality relationship between two variables is determined by its proportionality constant. The proportionality constant is the ratio of y over x.

I.e., k = y1/x1 = y2/x2 = y3/x3 = ... = yn/xn

The given data table is as follows:

x - 18.6, 54.3, 58.8

y - 6.2, 18.1, 19.6

So, the proportionality constant is calculated as

y1/x1 = 6.2/18.6 = 1/3

y2/x2 = 18.1/54.3 = 1/3

y3/x3 = 19.6/58.8 = 1/3

Since all three ratios are the same, then the data in the table are proportional to each other.

Therefore, option A is correct.

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The probability of rolling a number greater than 5 or doubles will be 0.78.

       P(A)  =  n(A)/n(S)

        where -

       n(A) = Number of outcomes favorable to event A.

        n(S) = Total number of outcomes.

We have two dices are rolled.

The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -

P(A) = 28/36 = 0.78

Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.

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[Question in english -

From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]

The measure of angle WZX is given as follows:

m < WZX = 41º.

The measure of angle XYZ is of 68º, hence, due to the bisection, we have that:

The measure of angle WXZ is of 71º, hence the measure of angle WXY is found as follows:

m < 2 x 71 = 142º.

(as the bisection of angle X means that it is divided into two parts of equal measure).

As the figure is a parallelogram, the opposite angles have the same measure, thus the measure of angle WZY is given as follows:

m < WZY = 142º.

Then, applying the bisection, the measure of angle WZX is given as follows:

m < WZX = 0.5 x 142º = 41º.

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Answer:

x^2 -10x + 41 = 0

Step-by-step explanation:

They gave you a root. A root is a solution, is a zero, is an x-intercept(if real).

This is a working backwards problem. They gave you an answer and want the equation back again.

x = 5 + 4i

working backwards:

x - (5 + 4i) = 0

x - 5 - 4i = 0

This left side is a factor of your equation.

If 5+4i is a root then 5-4i is also a root. So do the same thing:

x = 5 - 4i

x - (5 - 4i) = 0

x - 5 + 4i = 0

x - 5 + 4i and

x - 5 - 4i are the factors. Multiply them together to find the quadratic equation. Use distributive property or difference of squares or an area model to model. See image.

Answer:

x² - 10x + 41 = 0

Step-by-step explanation:

complex roots occur as a conjugate pair.

given x = 5 + 4i , then x = 5 - 4i is also a root

the corresponding factors are

(x - (5 + 4i) ) , (x - (5 - 4i) ) , that is

(x - 5 - 4i) and (x -5 + 4i)

the quadratic equation is then the product of the factors, that is

(x - 5 - 4i)(x - 5 + 4i) = 0

multiply each term in the second factor by each term in the first factor.

x² - 5x + 4ix - 5x + 25 - 20i - 4ix + 20i - 16i² = 0 ← collect like terms

x² - 10x + 25 - 16i² = 0 [ note i² = - 1 ]

x² - 10x + 25 + 16 = 0

x² - 10x + 41 = 0 ← in standard form

Principal will be $1000

Given values

Simple interest, SI= $800

Interest rate, R=8%

Time, T=10 months

Principle, P= Y

As we know;

[tex]Simple Interest, SI=P×R×T[/tex]

By substituting the values, we get

$800= Y ×8% ×10

$800=0.8Y

$800÷0.8= Y

$1000=Y

Thus the above response is correct.  

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Permutation test is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles

An estimation of the population distribution—the distribution from which our observations originated—is the goal of a permutation test. We can then calculate how uncommon our observed values are in comparison to the population.

I find the permutation test to be more natural, and it only relies on the assumption of random assignment of treatment groups.

In a permutation test, you compare the observed test statistic to the distribution of values

you get when the treatment group assignments are shuffled/randomized/permuted.

The null hypothesis that two distinct groups originate from the same distribution is tested using permutation tests, also known as exact tests, randomization tests, or re-randomization tests. A permutation test can be used for hypothesis testing or significance testing (including A/B testing) without requiring any presumptions to be made about the distribution of the samples, such as that the samples must be normally distributed.

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According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.

The equation is a mathematical statement or model that shows that two mathematical expressions are equal.

In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.

Cost of the new car = $25,000

Depreciation rate per annum = 20%

Value of the car = V

The price paid initially = P = $25,000

The annual rate of depreciation = r

Depreciation period = 4¹/₂ years

Equation model: V=P(1-r)^t

Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂

= $9,158.93

= $9,200

Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.

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