A supermarket increases the prices of some grocery items by 10%.

(a) What will be the new price of a loaf of bread marked at $1.80.

(b) What will the price of a packet of cereal that has a price tag of $4.20, but already discounted by 50%

Answer:

6

Step-by-step explanation:

If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.

I hope this helps!

I'm guessing the equation should read something like

[tex]7(x^2+y^2) \,dx + 5xy \, dy = 0[/tex]

or possibly with minus signs in place of +.

Multiply both sides by [tex]\frac1{x^2}[/tex] to get

[tex]7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0[/tex]

Now substitute

[tex]v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx[/tex]

to transform the equation to

[tex]7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0[/tex]

which simplifies to

[tex](7 + 12v^2) \, dx + 5xv\,dv = 0[/tex]

The ODE is now separable.

[tex]\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x[/tex]

Integrate both sides. On the left, substitute

[tex]w = 7+12v^2 \implies dw = 24v\, dv[/tex]

[tex]\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x[/tex]

[tex]\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x[/tex]

[tex]\dfrac5{24} \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex].

[tex]\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C[/tex]

[tex]\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)[/tex]

[tex]w^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]v[/tex].

[tex](7+12v^2)^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]y[/tex].

[tex]\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx[/tex]

Solve for [tex]y[/tex].

[tex]7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}[/tex]

[tex]\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}[/tex]

[tex]y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}[/tex]

[tex]y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}[/tex]

Answer: B

[tex]x + 2y \leq 4 \textrm{ and } 3x + y \leq 4[/tex]

Step-by-step explanation:

Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities

We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute

Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.

So we can eliminate both A and D since they both contain incorrect inequalities

Now, test the second inequality with x = 0 and y = 0

For B we get

3.0 + 0 = 0 which is indeed less than 4

C is not applicable since 0 is not greater-than-equal to 4

Hence B is the correct solution

This can be verified using a graphing tool (see image)

The angles ∠1 ≅ ∠4 since the line BD bisects ∠ABC, AD║ BC, and AB ║ CD. This is obtained by using the angle bisector theorem, alternate interior angles, and the transitive property of congruence.

Transitive property:

If ∠a and ∠b are congruent and ∠b and ∠c are congruent, then ∠a and ∠c are also congruent.

I.e., If ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c.

The angles bisector theorem states that the ray or line which bisects the angle divides the angle into two equal parts.

I.e., If line BD bisects the angle ∠ABC, then ∠B = ∠B1 + ∠B2

(where ∠B1 = ∠B2)

The line BD bisects ∠ABC, AD║BC, and AB║CD

The line BD bisects ∠ABC. So,

∠B = ∠3 + ∠4

According to the angle bisector theorem, ∠3 ≅ ∠4.

Since AD║BC and AB║CD, the alternate angle are congruent.

I.e., ∠3 ≅ ∠1

Thus, by the transitive property of congruence,

∠1 ≅ ∠4

Hence proved.

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Rotation is a transformation where an object is rotated about a fixed point.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation, reflection and rotation are rigid transformations because they preserve the shape and size of the figure.

Rotation is a transformation where an object is rotated about a fixed point.

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Answer:

the principal amount is 10000 is the rate of interest is 10 and the number of years is 10 you can calculate the simple interest a is equal to 10000 1 + 0 is equal to 1.6 is equal to 16000 interest is equal to a - b is equal to 6000 - 1000

Answer:

$1,760

Step-by-step explanation:

So I'm assuming the interest is simple interest rate which means that the interest applied each year is 12% of the original amount.

So this means that we can find the interest rate from one year by finding 12% of 800, and to do this we convert 12% to a decimal by dividing by 100 to get 0.12 and then use this decimal value to multiply by 800 to get: 0.12 * 800 = 96.

This means annually $96 will be charged in interest. To find how much interest there is after 100 years, simply multiply by 10, to get $96 * 10 = $960.

This is only the interest rate, it's like a fee, you still have to pay back the original amount, so all together you pay: $ borrowed + interest

So we add the interest rate 960 to the amount borrowed 800 to get: 960 + 800 = 1,760

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

we conclude that the system of inequalities has more solutions than the system of equations.

We have the system of equations:

y = (-1/2)*x + 1

y = x - 5

And the system of inequalities:

y > (-1/2)*x + 1

y < x - 5

First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.

Now let's look at the system of inequalities, we can get solutions like:

x = 10

y = 1

1 > (-1/2)*10 + 1 = -4

1 < 10 - 5 = 5

So both inequalities are true, which means that the point (10, 1) is a solution.

And also is the point (11, 1), and (12, 1), and infinite other points.

Then we conclude that the system of inequalities has more solutions than the system of equations.

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Answer:

9

(Correct On Edgen)

Answer:

It is the first graph

Step-by-step explanation:

The line under the > and < sign means that it must include the 3 and the 0.  The closed circle is showing that the 3 and 0 or included.

The mean of the scores to the nearest 10th digit will be 74.9.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.

Then the mean is given as,

Mean = (Total score) / (total student)

The total score will be

Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2

Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190

Total score = 2470

The total number of students will be

Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2

Total student = 33

Then the mean will be

Mean = 2470 / 33

Mean = 74.85 ≈ 74.9

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Answer:

  1,123,449,768

Step-by-step explanation:

The smallest number composed from 8 different digits that is divisible by each of those digits appears to be the 10-digit number ...

  1,123,449,768

If the number is to be divisible by an even digit, it must be even. That means it cannot end in the digit 5, so 5 cannot be one of the digits. We disallow division by 0, so 0 cannot be one of the digits.

The remaining 8 digits total 40, so cannot form a number divisible by 3, 6, or 9. In order to make such a number, we must add 5 to the digit total, but cannot do so using the single digit 5.

Choices for added digits include {1, 4} and {2, 3}. Adding 9+5 = 14 to the digit total would also work but would guarantee the resulting number is not the minimum possible.

The digits we have to work with are now {1, 1, 2, 3, 4, 4, 6, 7, 8. 9}. We know that an even number constructed from these digits will be divisible by 1, 2, 3, 6, and 9. To make it divisible by 4, 7, and 8, it must be a multiple of the LCM of those numbers.

The least possible number will use the smallest digits first, so will start ...

  112344...

The remaining digits, 6, 7, 8, 9, need to form a number that will be divisible by 56 when appended to the 6 digits already used. Those 6 digits form a number, 1123440000, that has a remainder of 32 when divided by 56. Hence we need to use the digits 6, 7, 8, 9 to make a number with a remainder of 24 when divided by 56. There are 24 permutations of the digits 6, 7, 8, 9. Half of these are odd numbers

The one number formed from digits 6, 7, 8, 9 that is divisible by 56 with a remainder of 24 is 9768.

The smallest number comprised of 8 different digits and divisible by each of them is the 10-digit number 1,123,449,768.

The factored expression of the polynomial is (4 - x)(5 + x)

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

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Answer: [tex]y=2x+2[/tex]

Step-by-step explanation:

[tex]2x+4y=8\\\\x+2y=4\\\\2y=-x+4\\\\y=-\frac{1}{2}x+2[/tex]

So, the slope of the given line is -1/2, meaning the slope of the line we want to find is 2.

Since the y-intercept is the given line is (0,2), the equation is [tex]y=2x+2[/tex]

The probability solved by binomial distribution that all will survive is 0.8154.

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Computation of probability of all survived people from heart attack;

A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).

What is the likelihood that each of the five patients who experience a heart attack will survive?

We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).

Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.

Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.

By binomial distribution,

[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]

Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).

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Answer:

blue dot have value of -6 in y inverse axis

Based on the railway timetable given, the time the first train reaches Oakengates is 0815.

The time taken to reach Shrewsbury from Telford Central is 22 minutes.

Oakengates is 2 minutes away from Telford Central so when a train leaves the latter and arrives at 0815, this is the first train to Oakengates.

If one left Telford Central at 0852, they would reach Shrewsbury at 0914 to make it:

= 0914 - 0852

= 22 minutes

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Answer:

- 4/7 , -1/9, 7/4

Step-by-step explanation:

You know that 7/4 is the largest number because it is the only positive number.  To compare the two negative numbers you need common denominators.  The common denominator would be 133 (19 x 7).  Now make equivalent fractions.-4/7 = x/133  133 divided by 7 is 19.  Multiple the -4 by 19 to get -76/133.  Next, make an equivalent fraction for -1/19.  The new denominator will be 133.  If I divide 133 by 19, I will get 7, so I multiple -1x7 and get -7 and the new fraction -7/133.

I have two fractions to compare -7/133 and -76/133.  -76/133 if farthest from 0 so it has the least value.

Answer:60g

Step-by-step explanation:

Hope this the answer

The system of equations best represents the number of apples a and the number of garonia bars g be a+b=60, 0.75x+0.15y=21.

Given that cost of 1 apple is $0.75, cost of 1 gargonia bars be $0.15 ,total things are 60 and total money paid be $21.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation.

Because we have been told that there are 60 total things and a represents the number of apples and g represents number of garonia represents the number of garonia bars.

a+b=60--------1

Money paid by consumers is cost per units*number of units

So,

0.75a+0.15b=21

Hence the system of equations best represent the number of apples and the  number of garonua bars g are a+b=60, 0.75a+0.15b=21.

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Answer:

  Slope = 7/4

Step-by-step explanation:

You are given coordinate values and a formula that tells you what to do with them. All you need to do is put the values in the formula and do the arithmetic.

You are given points (2, -3) and (6, 4). The slope formula refers to the two points as (x1, y1) and (x2, y2). It does not matter which is which.

If we use the points in the same order they are given, then we can see that ...

Using these values in the given formula, we find the slope to be ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-(-3)}{6-2}=\dfrac{7}{4}[/tex]

The slope of the line through the given points is 7/4.

The expression θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex] represents the family of all angles coterminal with - 50° angle.

Two angles are coterminal if and only if their end have the same direction. Two consecutive coterminal angles have a difference of 360°. Then, we can derive an expression representing the family of all angles coterminal to - 50° angle.

θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex]

The expression θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex] represents the family of all angles coterminal with - 50° angle.

The statement is incomplete and complete form cannot be reconstructed. Thus, we modify the statement to determine the family of angles coterminal to - 50° angle.

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Answer:

  a₄₅ = 13

Step-by-step explanation:

The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...

  aₙ = a₁ +d(n -1)

You want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...

  a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)

Evaluating this expression, we have ...

  a₄₅ = 2 +44/4 = 2 +11

  a₄₅ = 13

The 45th term of the sequence is 13.

The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

How to find the nth term of the Arithmetic series?

The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.

In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]

We have the find the forty-fifth term of the given series.

= [tex]Tn=a+(n-1)d[/tex]

= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]

= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]

= [tex]Tn = 2+11[/tex]

= [tex]Tn = 13[/tex]

So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

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The first equation is 5x² - 20x + 27 and the second equation will be y = 3x² + 6x + 15.

It should be noted that an equation simply means a formula that's used to express the equality of two expressions that are given in Mathematics.

It should be noted that before solving the equations, it's important to expand the functions that are squared and then solve accordingly. This will be illustrated below.

The first equation that's given is:

y = 5(x - 2)² + 7

= 5(x - 2)(x - 2) + 7

= 5(x² - 2x - 2x + 4) + 7

= 5(x² - 4x + 4) + 7

= 5x² - 20x + 20 + 7

= 5x² - 20x + 27

The second equation given is illustrated as:

y = 3(x + 1)² + 12

y = 3(x + 1)(x + 1) + 12

y = 3(x² + 2x + 1) + 12

y = 3x² + 6x + 3 + 12

y = 3x² + 6x + 15

In conclusion, writing the equations in form of y = ax² + bx + c will be y = 5x² - 20x + 27 and y = 3x² + 6x + 15.

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Sine rule:

30/sin(17) = x/sin(90)

x sin(90)

30 x sin(90) / sin(17) = x

x = 102.6091086

So, x = 102.6 to the nearest tenth.

Hope this helps!

Part 1

Angles in a triangle add to 180 degrees, so

[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]

Part 2

By the Law of Sines,

[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]

Answer:

What is the measure of angle E?

m∠E =

✔ 55

°

What is the length of EF rounded to the nearest hundredth?

EF ≈

✔ 12.49

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Equation of straight line in point - slope form :

[tex]\qquad❖ \: \sf \:y - y1 = m(x - x1)[/tex]

( m = slope = 4, point (5 , 17) )

[tex] \qquad◈ \: \: \sf \: y - 17 = 4(x - 5)[/tex]

[tex] \qquad◈ \: \: \sf \: y - 17= 4x - 20[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 20 + 17[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 3[/tex]

Now, it's the form of line in slope - intercept form, ( slope = coefficient of x = 4 and y - intercept = -3 )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \qquad◈ \: \: \sf \: y \: \: int = - 3[/tex]

Answer:

160 m³

Step-by-step explanation:

the volume of a rectangular prism is equal to :

= Base × height

= length × width × height

………………………………………

= 8 × 4 × 5

= 160

Note : the length can be 8 or 5

and the width can be 4 or 5