Choose the best estimate for the capacity of a bath tub. A. 5 ml B. 500 ml C. 50 cl D. 500 L

Answer:

[tex]a_{10}=124[/tex]

Step-by-step explanation:

In an arithmetic sequence, we are given that:

[tex]a_{17}=82\\d=-6[/tex]

The nth term of an arithmetic sequence, [tex]a_n=a+(n-1)d[/tex]

When n=17, [tex]a_{17}=82,d=-6[/tex], we have:

[tex]a_{17}=a+(17-1)(-6)[/tex]

82=a+(16)(-6)

82=a-96

a=82+96

a=178

Therefore, the 10th term of the sequence

[tex]a_{10}=178+(10-1)(-6)\\=178+9(-6)\\=178-54\\a_{10}=124[/tex]

Answer:

Step-by-step explanation:

the x-intercepts represent that the profit is $0

maximum value represents the highest profit which is $270

increasing intervals: (0, 4)

decreasing intervals: (4, 8)

in order to find the average rate of change, find the x and y coordinates for when x = 1 and x =4. The coordinates are (1, 120) and (4, 270). The average rate of change is basically the slope, which is (270-120)/(4-1) = 160/3= approximately 53.3333. The rate represents the change in profit in $ over the increase of cost of erasers.

As you can see, this a parabola, which consists of going up and down. The constraints of the domain represent that 4 is the best price for eraser because it yields the highest profit. The domain (x values) that are above and below 4 do not yield the best profit.

Answer:

The ratio is 2:3

Step-by-step explanation:

The first thing we need to get here is how much was paid for the Van in total.

That would be;

23,500 + 20% of 23,500

= 23,500 + (20/100 * 23,500)

= 23,500 + (23500/5)

= 23,500 + 4,700 = £28,200

She pays a deposit, which of course wasn’t stated in the question.

But we know she pays the rest in 18 equal payments at £940 each.

The total amount she paid asides the deposit would be :

28,200 -(940 * 18) = 28,200 - 16,920 = £11,280

So what this means is that she paid a deposit of £11,280 and a cumulative installment payment of £16,920

So now, we want to find the ratio of the deposit to the 18 equal parts payment.

Mathematically, that would be;

11,280 : 16,920

= 1128 : 1692

Divide both by 1128

= 1: 1.5

= 1: 3/2

which is same as 2:3

The ratio of the deposit Emma pays to a total of the 18 equal payments is 2/3 and this can be determined by finding the deposit amount and total amount paid for the Van.

Given :

Emma buys a camping van for £23500 plus vat at 20% she pays the deposit then pays the rest of the cost in 18 equal payments of £940 each month.

The total amount paid for the Van is:

[tex]= 23500 + \dfrac{20}{100}\times 23500[/tex]

= 23500 + 4700

= £28200

The total deposit amount is given by:

[tex]= 28200-18(940)[/tex]

= 28200 - 16920

= £11280

So, the ratio of the Emma pays to a total of the 18 equal payments is:

[tex]\dfrac{11280}{16920}=\dfrac{1128}{1692}[/tex]

Further, simplify the above ratio.

[tex]=\dfrac{2}{3}[/tex]

Therefore, the ratio of the deposit Emma pays to a total of the 18 equal payments is 2/3.

For more information, refer to the link given below:

https://brainly.com/question/15385899

Answer:

Step-by-step explanation:

In a quadrilateral all the angles equal to 360 degrees

ADC= 136+90+62=288.

360-288=72

A straight line is equal to 180 degrees

CDE= 180-72=108

x=108

Answer:

the value of x is 62 degrees.

Step-by-step explanation:

we know that corresponding angles are equal, so the value of x is 62 degrees as x is an corresponding angle of 62°

Answer:

  41%

Step-by-step explanation:

The table shows that 36 of the 88 students that like traveling out of state do not like camping. That percentage is ...

  36/88 × 100% ≈ 41%

Answer:

1/1001 < 4/10 < 49/100 < 357/10

Step-by-step explanation:

4/10 => 0.4

49/100 => 0.49

357/10 => 35.7

1/1001 => 0.0009

Ascending order is from smallest to the greatest.

Answer:

1/1001, 4/10, 49/100, 357/10

Step-by-step explanation:

Convert the fractions to decimals.

4/10 = 0.4

49/100 = 0.49

357/10 = 35.7

1/1001 = 0.0009

Arrange in ascending order.

0.0009, 0.4, 0.49, 35.7

Change back to fractions.

Answer:

The optimal side length for a storage area at the back corner of the property fenced on four sides and having an area of 100 m² is 10 meters

The optimal side length for a storage area attached to the back of their building fenced on three sides and having an area of 98 m² is 7·√2 m

Step-by-step explanation:

The optimal design to conserve building material will be to build the storage area to have equal sides which gives square shaped storage area

For a storage area at the back corner of the property fenced on four sides and having an area of 100 m², we have;

Storage area size = 100 m²

The number of sides = 4

The dimension of each side = Equal sides, s₁

Therefore we have;

s₁ × s₁ = 100

s₁² = 100

s₁ = √100 = 10 m

The side length = 10 m

For a storage area attached to the back of their building fenced on three sides and having an area of 98 m², we have;

Storage area size = 98 m²

The number of sides = 4

The dimension of each side = Equal sides, s₂

Therefore we have;

s₂ × s₂ = 98

s₂² = 98

s₂ = √98= 7·√2 m

The side length = 7·√2 m

Answer:

D=y=In x+5

Step-by-step explanation:

Answer: 56

Step-by-step explanation:

Let's organise our information :

The area of the cercle's quarter area is :

The area of the triangle is :

NOw the area of the shaded segment :

Answer:

1/7

Step-by-step explanation:

There are seven people in all on person will arrive at a different time than others. Every single one of them arrives at different times so it's 1/7

Answer:

152.4

Step-by-step explanation:

Answer:

A (3, 1)

B (2, 2)

C (1, 2)

D (1, 1)

Step-by-step explanation:

When a point is rotated 90° (90 degrees) counterclockwise about its origin, the coordinate B (x, y) transforms into B' (-y, x).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

Using the formula above B (x, y) ⇒ B' (-y, x), we have the coordinates for the polygon as:

A′ (-1, 3) ⇒ A (3, 1)

B′ (-2, 2) ⇒ B (2, 2)

C′ (-2, 1) ⇒ C (1, 2)

D′ (-1, 1) ⇒ D (1, 1)

∴  coordinates of the original polygon is given by the vertices:

A (3, 1), B (2, 2), C (1, 2), D (1, 1)

Answer:

40 students.

Step-by-step explanation:

There are 60 12th graders that voted for Nick and only 20 12th graders that voted for Garett. 60 - 20 = 40.

Hope this helps!

Answer:

C. h=3V/a^2 is the correct answer

Step-by-step explanation:

Given:

V=1/3a^2h

It can be rewritten as

V=1/3 *( a^2) * h

Divide both sides by (1/3)*h

V / (1/3*h) = (1/3)* (a^2) * h / (1/3)*h

V÷1/3*h = a^2

V÷3/1*h=a^2

3V/h=a^2

Multiply both sides by h

3V/h*h=h*a^2

3V=h*a^2

h=3V/a^2

C. h=3V/a^2 is the correct answer

Answer:

C

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The amount she withdrew is 45*4 =180

405 - 4*45=

405 -180 =225

There is 225 in the account

Answer: a) $225

Step-by-step explanation:

405 - 45 (4) = x

405 - 180 = x

225 = x

Answer:

The first option (5^2 + 8^2 = c^2).

Step-by-step explanation:

According to the Pythagorean Theorem, a^2 + b^2 = c^2.

If a is 5 cm, and b is 8 cm, you would have the following equation...

5^2 + 8^2 = c^2.

That matches with the first option.

Hope this helps!

Answer:

18.0

Step-by-step explanation:

==>Given:

Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°

==>Required:

Value of x to the nearest tenth

==>Solution:

Using the Cosine rule: c² = a² + b² - 2abcos(C)

Let c = x,

a = 16

b = 30

C = 30°

Thus,

c² = 16² + 30² - 2*16*30*cos 30°

c² = 256 + 900 - 960 * 0.8660

c² = 1,156 - 831.36

c² = 324.64

c = √324.64

c = 18.017769

x ≈ 18.0 (rounded to nearest tenth)

Answer: (√10)*a

Step-by-step explanation:

In a triangle rectangle, we have 3 sides, in this case, the shorter base, a, the longer base, b and the hypotenuse h.

And the hypotenuse can be found with the Pythagorean's theorem.

a^2 + b^2 = h^2

now, we know that b = 3a, then we can replace it in the above equation:

a^2 + (3*a)^2 = h^2

a^2 + 9*a^2 = h^2

10*a^2 = h^2

now we can apply the square root to both sides and get:

√(10*a^2) = √h^2

(√10)*a = h

Then we have found the length of the hypotenuse in terms of the shorter side a.

Answer: £6.80

Step-by-step explanation:

Kara bought 5 jumpers for the price of 4.  Thus, multiply 4.8*5 = 24.  Then divide 24/4 to get 6.

Hope it helps <3

Answer:

222222:#&&&#+17265262

Answer:

37,500

Step-by-step explanation:

0.2x+0.1(x−0.2x)=105000.2x+0.1(x−0.2x)=10500

0.3x−150x=105000.3x−150x=10500

15x−x50=1050015x−x50=10500

x=10500∗5014=1500∗25=37500

Step-by-step explanation:

Hello there!!

You can find it through simple way of ratio of sin or also by using cosine rule.

Lets do it simply as i can see your just 1st pic not second one so, i will answer you according to it.

so, here in question a Right angled triangle is given, with one angle 31° and one side 15 cm.

let's take sin angle as sin 31°.

so, p=h

h=15

We dont need base (b) here.

As we know that, thesin in ratio angle is

sin thita = p/h

or, sin 31°=h/15

or, 0.515038×15=h (using calculator sin 31°=0.515038.)

Therefore, the answer is 7.722557cm or 8cm.(as 7>5 and rounding off it we get 8).

Hope it helps...

The value of h in the right angled triangle is 7.7 cm.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

In the diagrams, using trigonometric ratio:

a) sin(31) = h/15

h = 7.7 cm

b) cos(24) = h/13

h = 11.9 cm

c) sin(37) = h/15

h = 9 cm

d) cos(47) = h/12

h =8.2 cm

e) sin(48) = h/18

h = 13.4 cm

The value of h in the right angled triangle is 7.7 cm.

Find out more on trigonometric ratio at: https://brainly.com/question/24349828

Answer:

C. and F.

Step-by-step explanation:

A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures. Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent. Right angle are 90 degrees

Answer:

C and F

Step-by-step explanation:

This triangle is not an equilateral triangle because their lengths are not equivalent to each other. It is not an isosceles triangle because no two lengths are equivalent to each other. It is a right triangle because it has one right angle(A 90 degrees angle.) It is not an obtuse triangle because there isn't an angle that is obtuse(More than 90 degrees but less than 180 degrees angle.) It isn't an acute triangle either because not all three angles are acute(Less than90 degrees angle.) Lastly, it is also a scalene triangle because none of the triangle lengths are equivalent to each other.

Answer:

The sum of all the sweets is 54 sweets

Step-by-step explanation:

Here, we want to calculate the number of sweets the three have altogether.

Let the number of sweet Faith has be x

Mathematically;

Faith has 4 sweets fewer than the average number of sweets

The average is the sum of all the sweets divided by 3

The average will be (10 + 30 + x)/3

Thus;

(10 + 30 + x)/3 - 4 = x

(40 + x)/3 = x + 4

40 + x = 3(x + 4)

40 + x = 3x + 12

40-12 = 3x -x

28 = 2x

x = 28/2

x = 14 sweets

So the sum of all the sweets would be 10 + 30 + 14 = 54 sweets

Answer:

Option A

Step-by-step explanation:

The median is the value that lies in the middle of the data when the data set is ordered.

It is also the value that separates the higher half of the dataset from the lower half of the dataset.

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A parent function is the simplest function that still satisfies the definition of a certain type of function. One of those functions is exponential, which is b.

   Option (B) will be the correct option.

We will check each option given for the definition of a parent function.

Option (A)

[tex]f(x)=-2^{x+1}[/tex]

Parent function will be,

[tex]f(x)=2^x[/tex]

Option (B),

[tex]f(x)=4^x[/tex]

It's a simplest form of an exponential function.

Therefore, it's a parent function.

Option (C),

[tex]f(x)=e^{3x}-2[/tex]

Parent function → [tex]f(x)=e^{3x}[/tex]

Option (D),

[tex]f(x)=4x^2[/tex]

Parent function → [tex]f(x)=x^2[/tex]

Learn more about the parent function and the transformation here,

https://brainly.com/question/11474649?referrer=searchResults

Answer:

A dilation was applied because the diameter of the circle decreased.

Step-by-step explanation:

Dilation is a process of either increasing or decreasing the size of a given figure without changing its shape. The resizing process make use of a scale factor to produce a dilated image of the given figure.

In the given question, it can be observed that the circle with center M has a diameter of 6 units, while that with center N has a diameter of 3 units. Thus circle M has been dilated with a scale factor of [tex]\frac{1}{2}[/tex] to produce circle N.

Therefore, a dilation was applied because the diameter of the circle decreased.

Answer:

I believe it is A

Answer:

17

Step-by-step explanation:

This is a very neat problem -- for teachers.

Let the number of sides = y

The sum of the interior angles is 180*(y - 2)

We are told that this sum equals 9x^2

So far the equation is

(y - 2)*180 = 9x^2                   Divide both sides by 9

(y - 2)*20 = x^2                       Remove the brackets on the left.

20*y - 40 = x^2

We need another fact. We get that from the statement that x is three greater than the number of sides (y). Therefore y = x - 3

20*(x - 3) - 40 = x^2

20x - 60 - 40 = x^2       Combine like terms on the left

20x - 100 = x^2             Bring the left side to the right side.

0 = x^2 - 20x + 100      You have a quadratic.

a = 1

b = - 20

c = 100

When you solve the quadratic equation, you get

x = 20

Therefore the number of sides is 17.

Answer:

D

Step-by-step explanation:

I'm not the greatest in this subject, but I think that it's D/If the roof leaks, then the ceiling gets damaged because it clearly says that in the statement. It could be all of them, though, but this is my answer. Hope it helps!

Answer:

D. If it rains, then the ceiling gets damaged.

Explanation:

So, if it rains, then the roof leaks, and if the roof leaks, then the ceiling gets damaged, is the exactly the structure of the syllogism law that permits to conclude if it rains, then the ceiling gets damaged.

Answer:

[tex]z=-0.842<\frac{a-30}{7.8}[/tex]

And if we solve for a we got

[tex]a=30 -0.842*7.8=23.432[/tex]

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

Step-by-step explanation:

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(30,7.8)[/tex]  

Where [tex]\mu=30[/tex] and [tex]\sigma=7.8[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.80[/tex]   (a)

[tex]P(X<a)=0.20[/tex]   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.20[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.20[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-0.842<\frac{a-30}{7.8}[/tex]

And if we solve for a we got

[tex]a=30 -0.842*7.8=23.432[/tex]

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

Answer:

z = 110°

Step-by-step explanation:

Since the figures are similar then corresponding angles are congruent, thus

∠ H = ∠ D = 110°, that is

z = 110°