Elin’s old fish tank is leaking. Diagram not drawn to scale This old fish tank is in the shape of a cuboid. The base of this tank measures 60cm by 40cm. Before the leak, the height of the water level in Elin’s old fish tank was 45cm. Elin decides to replace her fish tank with a cylindrical one. 70 cm Diagram not drawn to scale 25 cm She selects a new cylindrical fish tank that has a radius of 25cm and a height of 70cm. Will all the original contents, including the water and the fish, fit into this cylindrical tank? You must show all your working.

Answer:

u ≈ 5.7

Step-by-step explanation:

Using the Sine rule in Δ TUV, that is

[tex]\frac{t}{sinT}[/tex] = [tex]\frac{u}{sinU}[/tex] , substitute values

[tex]\frac{2.5}{sin26}[/tex] = [tex]\frac{u}{sin85}[/tex] ( cross- multiply )

u × sin26° = 2.5 × sin85° ( divide both sides by sin26° )

u = [tex]\frac{2.5sin85}{sin26}[/tex] ≈ 5.7 ( to 1 dec. place )

Answer:

2 rational solutions

Step-by-step explanation:

the degree of the polynomial (the highest exponent of the variable) defines how many solutions there are.

that means for how many values of x the result y is 0 (how many x-axis interceptions there are or should be).

so, a quadratic equation has 2 such solutions.

there are a few different cases how these solutions present themselves :

"normal case" : all the solutions are real (not only rational) numbers, and the curve has that many different x- acid interceptions.

a turn of the curve leads to only "touching" the x-axis : this is just a special case that the curve is "too high" or "too low" and the regular 2 intersects merge into 1. there are formally still 2 solutions, but they are identical.

there can be "S-curves" especially for higher degrees (3 and up) with the center smoothing in with the x-axis : this is similar but can merge even more than 2 solutions into 1.

the curve is really "too high" or "too low" and never even touches the x-axis : then the solutions are irrational.

the general solution for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

the discriminate is (b² - 4ac).

if this is a positive perfect square, then the square root is a perfect integer. in fact, 2 perfect integers (+ and -).

and so we get two solutions with integer/integer and they are therefore 2 rational solutions.

Answer:

A) Se requiere una tabla con una longitud de 2.213 varas para fabricar la mesa.

B) El lote de José tiene una extensión de 536.481 varas cuadradas.  

Step-by-step explanation:

A) La vara es una unidad de longitud equivalente a 0.836 metros. También sabemos que un cuadrado es una figura geométrica con cuatro lados de igual longitud y cuatro ángulos rectos, de modo que la longitud y ancho de la mesa es igual. Entonces, el largo de la tabla, esto es, la superficie superior de la mesa, tiene una medida de 1.85 metros.

A continuación, realizamos la regla de tres para determinar su equivalente en varas:

[tex]x = 1.85\,m\times\frac{1\,vara}{0.836\,m}[/tex]

[tex]x = 2.213\,varas[/tex]

Se requiere una tabla con una longitud de 2.213 varas para fabricar la mesa.

B) La vara es una unidad de longitud equivalente a 0.836 metros. Una vara cuadrada es una unidad de área y es igual a:

[tex]r = (0.836\,m)\cdot (0.836\,m)[/tex]

[tex]r = 0.699\,m^{2}[/tex]

De manera semejante, tenemos que el área del lote de Jose es un rectángulo y que se calcula como sigue en metros cuadrados:

[tex]A = l\cdot w[/tex] (Eq. 1)

Donde:

[tex]A[/tex] - Área del lote de José, medido en metros cuadrados.

[tex]l[/tex] - Largo del lote de José, medido en metros cuadrados.

[tex]w[/tex] - Ancho del lote de José, medido en metros cuadrados.

Si [tex]l = 25\,m[/tex] y [tex]w = 15\,m[/tex], entonces el área del lote es:

[tex]A = (25\,m)\cdot (15\,m)[/tex]

[tex]A = 375\,m^{2}[/tex]

Por último, hallamos el área en varas cuadradas mediante la siguiente regla de tres:

[tex]x = 375\,m^{2}\times \frac{1\,vara}{0.699\,m^{2}}[/tex]

[tex]x = 536.481\,varas^{2}[/tex]

El lote de José tiene una extensión de 536.481 varas cuadradas.  

Answer:

15

Step-by-step explanation:

x+(x+1)+(x+2)= 48

=)3x+3=48

=)3x=45

X=15

The smallest of the integers would be 15.

The consecutive numbers are those numbers that follow each other continuously in the order from smallest to largest numbers.

Given that the sum of 3 consecutive integers is 48.

We need to find the smallest of the integers.

Let assume the 3 consecutive integers are x, (x+1) and (x+2)

Therefore, x+(x+1)+(x+2)= 48

Combine the like terms;

3x+3=48

3x=45

X=15

Hence, the smallest of the integers would be 15.

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Answer:

8 km

Step-by-step explanation: giving that

distance=10km

time=75 minutes =75/60 hours

                                15/12=5/4 hours

speed=disance=10km

             time     = 5/4hours

     =40/5km/hours

    =8km/hours

Answer:

please mark me the brainlist

Step-by-step explanation:

please mark me as brainlest

Answer: 32

Step-by-step explanation:

This is an example of an arithmetic sequence as the difference between the first 3 terms is constant. We can see that 4 is constantly being subtracted.

[tex]a_{n}=a+(n-1)d[/tex]  is the formula for an arithmetic sequence.

[tex]a_{n}[/tex] = nth term

a = the first term in the sequence

n = term you are looking for (in this case 45)

d = common difference between the terms (in this case -4)

∴

[tex]a_{n}=a+(n-1)d[/tex]

[tex]a_{45} =208+(45-1)(-4)\\a_{45}=32[/tex]

Answer:

4x+y=-4

Step-by-step explanation:

gradient(m)=y2-y1/x2-x1

the line also passes through points (x,y) and (-2,4)

-4=4-y/-2-x

cross multiplying

8+4x=4-y

option(A):4x+y=-4

is your answer.

Answer:   a. the slope is -2/5 and the y-intercept is -1/3

Step-by-step explanation:

Find the slope by finding the difference in x-values divided by the difference in y-values

(1/4 ,-13/30) and (-3/4, -1/30)  are useful values

-13/30 --1/30 = -12/30    = -2/5 is the rise      

-1/4 - -3/4 = 1  is the run (-2/5)/1 Division by 1 leaves the original numerator)

the slope is -2/5

To find the y intrcept, substitute the y and x values from any given coordinate into the slope intercept form and solve for  b

y= mx + b

-3/5 = (-2/5)(2/3) + b

-9/15 + 4/15 = b

-5/15 = b

-1/3 = b  This is the y-intercept

Screenshot below of graph illustrates this solution

Answer:

28

Step-by-step explanation:

probability of getting blue ball is 4/9

total cases = 72

i.e number of blue ball 32

number of red vall is 40

so extra 28 is added

Answer:

6

Step-by-step explanation:

Answer:

x

Step-by-step explanation:

The composition of a function and its inverse is x.

Answer:

50 gold coins

Step-by-step explanation:

5%=5/100

therefore 5% of 1000

=5%×1000

=5/100×1000

final answer would be 50 coins...

Answer:

Step-by-step explanation:

Let's find the LCM of 5 and 6. 5x6 is 30. So 1/5 times 6 to both numerator and denominator is 6/30. 1/6 is slightly different. 30 is 5 times 6. So 1/6 times 5 to both denominator and numerator is 5/30. Since 6/30 and 5/30 does not have a halfway point, let's multiply both by 2. It is 10/60 and 12/60. Midway point is 12+10/2 which is 11/60.

Answer:11/15

1/5+1/6=11/30

11/30 /2=11/15

11/15

Step-by-step explanation:

Answer:

540 miles

Step-by-step explanation:

450/15 = 30

so the car can travel 30 miles per gallon

18*30 = 540

Answer:

540 miles

Step-by-step explanation:

Gallons:     15          18

Miles:        450         x  

450 divided by 15 = 30

18 times 30 = 540

Answer:

0.102542

Step-by-step explanation:

Given that 9% of customers do not provide a reason, 29% say the item did not fit, 13% find a flaw with the item, and 4% changed their mind about the purchase.

So, the total percentage of items returned due to no reason, unfit, flaw, and due to changing mind

=9%+29%+13%+4%=55%

As the remaining customers returned gifts purchased for them, so, the percentage of customers who returned gifts =100-55=45%.

So, the fraction of customers who returned gifts=45/100=0.45.

Now, observe that if 1 item returned, there is a chance of 0.45 that the item is a gift.

Moreover, there are only two possibilities for any idem, i.e the idem was a gift or not a gift, so the number of total returned items can be considered a Bernoulli's population.

Let p be the probability of a returned item which is the same for all the returned items,

p=0.45

So, according to Bernoulli's theorem, the probability that out of n=40 returns on a given day, r=20 are gifts is

[tex]\binom{n}{r}p^r(1-p)^{n-r}=\binom{40}{20}(0.45)^{20}(1-0.45)^{40-20}[/tex]

[tex]=0.102542[/tex]

Hence, the probability that 20 returned items are gifts among the total 40 returned items is 0.102542.

Answer:

a. All sides are the same length

a. 60 degree for each angle

b. Parallelogram, rhombus

c. trapezoid

The total balance of Greg account after he makes the monthly payment for July is $864.99.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

It can be calculated with the following formula.

[tex]M=P\left(1-\dfrac{r}{1-(1+r)^{-nt}}\right)[/tex]

Here, (P) is the principal amount, (r) is the interest rate and (t) is time.

Greg has a credit card which requires a minimum monthly payment of 2.06% of the total balance.

His card has an apr of 11.45%, compounded monthly. At the beginning of May, Greg had a balance of $318.97 on his credit card.

In the Month of May he make payment of 46.96, 33.51, and 26.99. Greg had a balance of $318.97 on his credit card. The total balance after the end of may is,

[tex]P=46.96+33.51+26.99+318.97\\P=426.43[/tex]

The financial charge on this payment with Apr 11.45% is 4.07. Thus, the payment become 430.5.

The payment for the June 97.24, 112.57,72.45. The payment at the end of June is 719.56 and financial charge is 10.22.

The payment become 722.98. The payment for the June 41.14, 101.84. At the end of July 865.96.

The total balance of Greg account after he makes the monthly payment for July is $864.99.

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Answer:

he will have enough money for thirteen people

Step-by-step explanation:

because $15*13 people =$195 . he will have extra $5 dollars to go home

Answer:

250

Step-by-step explanation:

add all numbers which gives the number

we can see the point ( - 1 ; - 2) on the line

so

f(-1) = - 2

as a point is ( x ; f(x) )

Answer:

f(-1) = -2

Step-by-step explanation:

f(-1) means find the value at x = -1

The y value at x=-1 is -2

f(-1) = -2

Answer:

Direct

Step-by-step explanation:

16/4 = 4

100/25 = 4

4 = 4

Answer: ( D) 998 is the greatest three digit positive integer

Step-by-step explanation: Your welcome.

Answer:

y - 5 = -3(x - 12)

Step-by-step explanation:

Point slope form is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Plug in the point and the slope:

y - y1 = m(x - x1)

y - 5 = -3(x - 12)

So, y - 5 = -3(x - 12) is the equation in point slope form of the line.

Answer:

y-5 = -3(x-12)

Step-by-step explanation:

Answer:

26.22 foot

Step-by-step explanation:

The relation between foot and meter is given by :

1 foot = 0.305 meter

We firstly find value of 1 meter in terms of foot.

So,

[tex]1\ m=\dfrac{1}{0.305 }\ \text{foot}[/tex]

To find no of foot in 8 meters, multiply [tex]\dfrac{1}{0.305 }[/tex] by 8 i.e.

[tex]8\ m=\dfrac{1}{0.305 }\times 8\ m\\\\=26.22\ \text{foot}[/tex]

So, there are 26.22 foot in 8 meters.

Answer:

3?

Step-by-step explanation:

3(264621(305613

8829. (101871

The Highest Common Factor of 264627 and 305613 is 891.

The highest common factor (HCF) is found by finding all common factors of two numbers and selecting the largest one.

For example, 8 and 12 have common factors of 1, 2 and 4. The highest common factor is 4.

Given:

264627 and 305613

Now, prime factorizing both number

264627  = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 11 x 11

and, 305613 = 3 x 3 x 3 x 3 x 7 x 7 x 7 x 11

So, the common factors are 3 x 3 x 3 x 3 x 11 = 891

Hence, the HCF is 891.

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Answer:

100 bags

Step-by-step explanation:

Simply add 30 + 15 + 5 and we get 50

Next divide 50 by the amount of lbs we want 50/0.5 = 100

Answer:

3 classmates

Step-by-step explanation:

1/9 = 0.111111...

27 x 1/9 = 3