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Scorpion4ik [409]

3 years ago

6

a hat contains 3 blue and 5 black tickets. if one ticket is chosen at random from the hat what is the probability that it is blu

e?

1 answer:

Nikitich [7]3 years ago

3 0

Answer:

3/8

Step-by-step explanation:

3/(3 + 5) = 3/8

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Small notebooks cost $3.50 and large notebooks cost $5.00. She needs to buy 31 notebooks, and she has $134 to spend. How many sm

Darina [25.2K]

Let's assume

number of small notebooks =x

number of large notebooks =y

we are given

total number of notebooks =31

so, we get

$x+y=31$

now, we can solve for y

$y=31-x$

we have

Small notebooks cost $3.50 and large notebooks cost $5.00

she has $134 to spend

so, we get

$3.50x+5y=134$

now, we can plug y

$3.50x+5(31-x)=134$

$3.50x+5*31-5x=134$

$-1.5x+155=134$

$-1.5x+155-155=134-155$

$x=14$

now, we can find y

$y=31-14$

$y=17$

so,

number of small notebooks is 14

number of large notebooks is 17.............Answer

6 0

3 years ago

Read 2 more answers

Three times a larger number is 30 more than 5 times a smaller number. The sum of the larger number and 5 times the smaller numbe

kicyunya [14]

Answer: Smaller number = 6

Larger number = 20

Step-by-step explanation:

Let the smaller number be x.

Let the larger number be y.

Three times a larger number is 30 more than 5 times a smaller number. This will be:

3 × y = (5 × x) + 30

3y = 5x + 30 ...... i

The sum of the larger number and 5 times the smaller number is 50. This will be:

y + 5x = 50 ...... ii

From equation ii

y + 5x = 50.

y = 50 - 5x ...... iii

Put the value of y = 50 - 5x into equation i

3y = 5x + 30

3(50 - 5x) = 5x + 30

150 - 15x = 5x + 30

150 - 30 = 5x + 15x

120 = 20x

x = 120/20

x = 6

The smaller number is 6

Note that y + 5x = 50

y + 5(6) = 50

y + 30 = 50

y = 50 - 30

y = 20

The bigger number is 20

7 0

3 years ago

Mr. Majors ordered six hot dogs and a bucket of popcorn at the concession stand. If the popcorn

Hoochie [10]

Answer:

The cost of one hot dog is $2.50

Step-by-step explanation:

You need to subtract $3.20 from $18.20 to get $15.00. Then you need to divide $15.00 by 6 to get $2.50.

3 0

3 years ago

Anna inherits $70000 and decides to invest part of it in an education account for her daughter and the rest in a 5 year CD. If t

TEA [102]

E = amount she put for Education

CD = amount she put for a Certificate of Deposit.

so, whatever those amounts are, we know that all she got is 70,000 bucks total, so E + CD = 70000.

how much is three times the CD? well, 3*CD or 3CD.

how much is 10,000 more than that? well 3CD + 10000.

since we know that the amount on Education was 10000 more than three times the CD, then E = 3CD + 10000.

$\bf \begin{cases}
E+CD=70000\implies \boxed{CD}=70000-E\\
E=3CD+10000\\
------------------\\
E=3\left( \boxed{70000-E}\right)+10000
\end{cases}
\\\\\\
E=210000-3E+10000\implies 4E=200000\implies E=\cfrac{200000}{4}
\\\\\\
E=50000$

how much was it invested in the CD? well, CD = 70000 - E.

5 0

3 years ago

Read 2 more answers

Let f(x) = -5x^6√x + -7/x³√x. What would f’(x) be? If anyone could show me step-by-step, I would greatly appreciate it! I’ve wor

Illusion [34]

Answer:

$f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}$

or

$f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}$

Step-by-step explanation:

Rather than solving this question in a more complex method by directly using the product rule and quotient rule, it can first be considered to perform some algebraic manipulation (index laws) to simplify the expression before taking the derivative.

$\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^6\ \sqrt{x}\ +\ \frac{-7}{x^3\ \sqrt{x}}\\\\f\left(x\right)\ =\ -5x^6\cdot x^{\frac{1}{2}}\ +\ \frac{-7}{x^3\cdot x^{\frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{6\ +\ \frac{1}{2}}\ +\ \frac{-7}{x^{3\ +\ \frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ +\ \frac{-7}{x^{\frac{7}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\end{array}$

Now, the derivative of the function can be calculated simply by only using the power rule, which yields

$\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\\\\f^{\prime}\left(x\right)\ =\ \left(-5\right)\left(\frac{13}{2}\right)\left(x^{\frac{13}{2}\ -\ 1}\right)\ -\ \left(7\right)\left(-\frac{7}{2}\right)\left(x^{-\frac{7}{2}\ -\ 1}\right)\\\\f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}\\\\f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}\end{array}\\\end{large}$

8 0

2 years ago